Very likely, it took Euclid a bit longer than 15 minutes to invent this brilliant algorithm. I am thankful that I can learn his algorithm in under 15 minutes, thoroughly explained and easy to understand. Thanks you for that, Math with Jay.
@@geraldillo "it took Euclid a bit longer than 15 minutes to invent this brilliant algorithm." Citation? It took ~15 minutes to run through 1 example. Presumably, he needed longer to come up with a general solution, check it, and prove it?
I searched so long for a proper explanation to this topic and you literally made me understand one week of college classes in 15 minutes! Keep up the good work and thank you kindly! 😊
Thank you so much! It always baffles me that teachers such as yourself can explain things this clearly and concisely, whilst others would take weeks to convey the same message.
12:36 Im so confused how 12*17x = x?? I understand thats what weve found for Bezut, but I just dont get how this works to isolate x? Is there some implicit thing we must assume about the 12? Because outright 12*17x could never give x.
Precisely explained; my Discrete Mathematics professor is basically useless. I'll be finding myself in this channel quite often through out the rest of the semester.
Damn! I searched every playlist, saw nearly every video on this topic, and when I watched this one. I knew something extraordinary struck my mind! The question was solved!! A HUGE THANKS to you. The way you taught and explained each process is mesmerizing! I got each and every step so easily that I won't be forgetting it for a decade or such!
I dont even study in English but couldn't find an Explanation in my language. Thanks so much for uploading this. Finally understood why we can Change it into a linear equation!!
Exceptional video! I like how each step is mentioned, by far the best video I've seen. @3:07 in the video I believe the side equation should read: 17v = 1 + 29w --> 17v - 29w = 1. Otherwise, the equation doesn't equate to 1.
Hi I want to ask what steps would be taken if the result of v after using the extended algorithm was a negative integer. would you still proceed using the outlined steps??
The first stage here is to divide through by the common factor. Then v will will be negative, so x will also be negative, but you can then add on a positive multiple of the mod so that your final answer is a small positive value. You can then check that it solves the given congruence. What do you get for v?
thanks for your help thus far these the values i got for v and w : v=-21 and w=5. so i'm confused on how to proceed from there because of the presence of the negative sign.
You are doing fine: you now know that 14x is congruent to 25 (mod 59), and 1 = 5x59 - 21x14, so (-21) multiplying both sides of your linear congruence gives x= -525. Add 9x59 to this to get a small x value. Or if you don't like (-21), you could add 59 to it to get 38 and use that instead....then you'd get 950 before subtracting a multiple of 59. Both methods give the same value for x...and check this in your original congruence.
@@MathsWithJay I couldn't understand why 12*17 congruent to 1, then 12*17*x congruent to 12*3 mod(29) then x congruent to 12*3 (mod29) how could you cancel out. What formula that you used
I have one more question, I am doing a RSA encryption problem. and I want to know how to solve bigger number modular without fast modulation. For ex: 2015^17 mod (3233) how would I break down the number and exponentials?
@ImDHML: One way to start on a similar example: If we want 2018^19 (mod 3104), this would be congruent to (-1086)^19 (mod 3104), then it might help to write 1086 as 2x3x181, ...
Great video, but just one question(I'm dumb), as the result of x congruent 7(mod 29), wouldn't that means x-7=29k?(k is a random number that representing the times of 29), I'm kinda confused cuz the way you check the result is kinda like taking "x=7" instead of "x congruent 7"
I was stuck with why the multiplication if x*n becomes just x, but now I understand why, I just couldn't see it because my professor thinks it's obvious matter. Thank you!
Yep! It's called "explaining complex concepts with few clear steps instead of throwing a bunch of formulas and hoping your students will figure it out". Altought, you can't find it in drug stores. It's quite rare...
OK. I am lost at the last step. How did you go from X is congruent to 36 (Mod29) to Xi s congruent to 7 (Mod29)? Please show steps when responding. Thank you.
Maths with Jay it doesn’t exactly have two negative solutions, but solving 5x congruent to 9mod8 gave me v = -3 and w = 2, so I’m a bit confused how to solve the last part (the part after we calculate v and w ) and how to check the answer if the v is negative
You could make v positive by adding on 8 because you are using mod 8. (You could also make the question simpler by subtracting 8 from 9) Both should give the same answer.
very nice :) .. but what if i have something like 21x=11mod3 (by = i means to congruent) so (21,3) dos not divide 1 . but this linear congruent is a part of Chinese remainder theorem problem..
17x ≡ 3 mod 29 => -12x ≡ 3 mod 29 Now divide by 3 to get: -4x ≡ 1 mod 29 What multiple of 29 must I add to 1 to get a multiple of 4? 29 mod 4 ≡ 1, so subtract 1 multiple of 29: -4x ≡ -28 mod 29 Now divide by -4: x ≡ 7 mod 29 The general solution is x = 7 + 29n.
this does not work on every linear congruent right? I mean.... I tried the method yes, but I also used the "Linear Congruence Calculator" and they have different results, idk why and idk which is correct or not.
I could have started with 20x + 1 ≡ 3x + 4, and then subtracted 3x and 1 from both sides. I could check the answer in 20x + 1 ≡ 3x + 4..and see that it works.
when you said 17v is congruent to 1 (mod 29), is that true because 29 is prime, in other words if it was 17x is congruent to 3 (mod 30), would it still be correct to write 17v is congruent to 1 (mod 30)?
17v is congruent to 1 (mod 29) because we worked out that 17x12 - 7x29 = 1. If you want to use mod 30, you need to start at the beginning again, using 30 instead of 29.
Can also solve with 17x-3 = 29k. Try different values of k, i.e. 0,1,2,... until you get an integer solution for x. With k=4, then x=7. Much easier for small values of k. Otherwise, not practical without a computer.
Your video was amazing thank you very much! Just one quick question, let's say that in the end, the result was x congruent 14 (mod 19). Would x be equal to 14 or 5 (as 19-14= 5 but it is not arranged in that order)?
Thank you for your feedback, Aimee. You can add or subtract multiples of 19 from 14, so the best answer is 14, but 14 - 19 = -5 is also an answer. 5 is not congruent to 14 (mod 19).
Well, it's an interesting algorithm, but intuitively, it doesn't feel right unless you have a grasp of the underlying arithmetic. Everybody should try at least once to solve the equivalent Diophantine equation by the usual method - you'll find that the amount of computation is the same, and you'll feel more confident with the Euclidean Algorithm. In this case, we want to solve the Diophantine equation 17x = 29a + 3 where x, a are integers. We proceed by consecutive substitutions, each one of which is an integer. Notice how the denominator reduces in size at each step: x = (29a+3)/17 = a + (12a+3)/17 then let b = (12a+3)/17 which must be an integer if x and a are integers as we require. Then we rearrange: a = (17b-3)/12 = b + (5b-3)/12 then let c = (5b-3)/12 b = (12c+3)/5 = 2c + (2c+3)/5 then let d = (2c+3)/5 c = (5d-3)/2 = 2d - 1 + (d-1)/2 [_For the final step I'll use n as the integer (because e might cause confusion)_] then let n = (d-1)/2 which gives d = 2n+1 Each consecutive integer n will then generate solutions. So we can now substitute for d to get c in terms of n, then express b in terms of n, and a in terms of n and finally x in terms of n: c = (5d-3)/2 = (5(2n+1)-3)/2 = 5n+1 b = (12(5n+1)+3)/5 = 12n+3 a = (17(12n+3)-3)/12 = 17n+4 x = (29(17n+4)+3)/17 = 29n+7 Notice how the arithmetic is equivalent to that presented when following Euclid's Algorithm in the video. The solutions are just the same and you can of course check by trying values of n from 0, 1, 2 ... etc. which will each generate a value for x that when multiplied by 17 and divided by 29 will leave a remainder of 3. Working through this kind of "primitive" method may well have been the basis for Euclid's insight into the deeper properties of congruence arithmetic.
Wow! God bless you. My class was moved to an online class due to COVID-19 and I have been struggling so much with this because nobody thoroughly explains it like you just did. Thank you so much.
Bonjour, Solving such equations are much more simply by the pattern of Ouragh . Indeed for the equation treated in the video this scheme is as following .....29........17........12.........5.........2.........1 ..................-1.........-1.........-2........-2 .................12.........-7..........5........-2.........1 and so we have x is congruent to 12 * 3 [ 29] is x = 7 [29] Cordially.
3 - 2, so 1 (mod 5) Try putting a number in for x, so if x is 4 for example, 3x is congruent to 12, so congruent to 2 mod 5 and 3x + 2 would be congruent to 4, then you can see what happens when you add or subtract 2 from both sides
On this topic, this is arguably the best explanation. Thank you.
Brilliant! Thank you very much
can someone explain to me how the 4 is removed?
Best with 1.25 speed :)
+Moontego :)
Better than best with 2.00 speed, a whiteboard, and lots of pausing.
Very likely, it took Euclid a bit longer than 15 minutes to invent this brilliant algorithm. I am thankful that I can learn his algorithm in under 15 minutes, thoroughly explained and easy to understand. Thanks you for that, Math with Jay.
My pleasure, geraldillo
@@geraldillo "it took Euclid a bit longer than 15 minutes to invent this brilliant algorithm."
Citation? It took ~15 minutes to run through 1 example. Presumably, he needed longer to come up with a general solution, check it, and prove it?
I searched so long for a proper explanation to this topic and you literally made me understand one week of college classes in 15 minutes! Keep up the good work and thank you kindly! 😊
Excellent. So glad that you found this useful!
Thank you for the clear explanation of this. I'm taking a discrete math class currently and the book did not explain very well.
Thanks a lot for your useful feedback.
Thank you so much! It always baffles me that teachers such as yourself can explain things this clearly and concisely, whilst others would take weeks to convey the same message.
You're very welcome!
12:36 Im so confused how 12*17x = x?? I understand thats what weve found for Bezut, but I just dont get how this works to isolate x? Is there some implicit thing we must assume about the 12? Because outright 12*17x could never give x.
We found that 12*17=1 on the LHS of the screen
Precisely explained; my Discrete Mathematics professor is basically useless. I'll be finding myself in this channel quite often through out the rest of the semester.
Welcome to Maths with Jay!
I didn't learn this in Discrete Math.
Damn! I searched every playlist, saw nearly every video on this topic, and when I watched this one. I knew something extraordinary struck my mind! The question was solved!! A HUGE THANKS to you. The way you taught and explained each process is mesmerizing! I got each and every step so easily that I won't be forgetting it for a decade or such!
@Prashant: Thank you so much for this lovely feedback. It's great to know that you found this video so useful.
Which method is the most efficient in solving the linear congruence?
I'am german and i never understand a german Video about Linear Congruence. Now i understand it... Awesome work! :)
Glad to hear that! I speak a little German, but not enough to explain maths!
Very Nice. Brilliantly explained, and nice and slow!! Thank you!!
Thank you, Lewis. Glad you found it useful!
3:08 why is it minus 29??
It could be plus or minus...if you try it with plus, w will end up having the opposite sign
I dont even study in English but couldn't find an Explanation in my language.
Thanks so much for uploading this. Finally understood why we can Change it into a linear equation!!
Thank you! What is your language?
German :)
Danke!
At 2:46 how did you write 17v=1-29w
I don’t understand that too
Think about what mod 29 means...
Exceptional video! I like how each step is mentioned, by far the best video I've seen.
@3:07 in the video I believe the side equation should read: 17v = 1 + 29w --> 17v - 29w = 1. Otherwise, the equation doesn't equate to 1.
Thank you for your feedback. We have 17v = 1 - 29w ...but a different sign in front of the 29w just means that we would find w has a different sign.
What if the left hand side has subtraction or addition like 3x − 5 ≡ 4 (mod 7)?
You can treat it like a normal equation, so add 5 to both sides
This is the 4th video on this topic and I finally understood it.. thank you
You're very welcome!
Wow this video is very helpful for me...i have cleared my doubt from this video thank you so much ma'am.
Most welcome 😊
In less than 15 minutes, you've managed to explain what my professor failed to in 50. Thank you.
@Caleb: Thank you!
Thanks Jay! most useful 14 minutes ever!
Thank you!
A GREAT explanation, easy to follow while writing what you're saying. Thank you for it, love ya!
+Islam Elshobokshy Thank you so much for your positive feedback. It's great to know that you found this so useful.
Jay
right at the end, congruent to 1. whats that mean? how does 12(17x) = x?
@Colin: Multiply 12 by 17...this gives 204....divide by 29....what is the remainder?
this what I call a top notch explanation, thank you
Thank you so much for your positive feedback
Your voice is really smooth, i like it!
You completely lost me at 08:49. How does 5-2x12+4x5 = 5x5-2x12? Surely it should equal 5-24+20. Am I wrong?
5 = 5x1, and so we have 5 times (1 + 4), so 5x5. You are correct too, but its not in a useful format...
omg why do i go to lecture when i can come here. THANK YOU JAY
Thanks a lot :)
Hi I want to ask what steps would be taken if the result of v after using the extended algorithm was a negative integer. would you still proceed using the outlined steps??
It's easier to answer this kind of question if you give an example. If you are not sure if the method works, try it, then check the answer at the end.
thanks for your response here is the problem I was trying to solve 56x is congruent to 100 mod 236.
The first stage here is to divide through by the common factor. Then v will will be negative, so x will also be negative, but you can then add on a positive multiple of the mod so that your final answer is a small positive value. You can then check that it solves the given congruence. What do you get for v?
thanks for your help thus far these the values i got for v and w : v=-21 and w=5. so i'm confused on how to proceed from there because of the presence of the negative sign.
You are doing fine: you now know that 14x is congruent to 25 (mod 59), and 1 = 5x59 - 21x14, so (-21) multiplying both sides of your linear congruence gives x= -525. Add 9x59 to this to get a small x value. Or if you don't like (-21), you could add 59 to it to get 38 and use that instead....then you'd get 950 before subtracting a multiple of 59. Both methods give the same value for x...and check this in your original congruence.
Very much helpful to students in secondary levels.
@GajendraPrasad Das: Thank you! What age are those students and in which country?
Finally found the best explanation, thank you very much
You are welcome!
Great explanation. Keep up the good work (Y)
+Siddhant Sharma Thank you for your positive feedback; it is much appreciated.
Jay
Amazing!!! you made the process very simple.
Great to have your feedback. Thank you.
I love this explanation, thank you very much. Hugs from México!
@Goa: Many thanks! Greetings to México from London!
I can't find the word to explain how good this video was! Thank you so much! (I'm not english sorry for my mistakes)
@Simone: Thank you very much! Your English is very good.
How did 12*17 is congruent to 1 leave with just x please explain further
@Ian: At what time in the video please
Maths with Jay @12:58 is there a theorem that makes it only x on the LHS?
@Ian: Look at the working on the bottom of the left of the page: we have just shown that 17x12 is congruent to 1, so 12x17 is also congruent to 1.
Maths with Jay thank you so much!!!
@@MathsWithJay I couldn't understand why 12*17 congruent to 1, then 12*17*x congruent to 12*3 mod(29) then x congruent to 12*3 (mod29) how could you cancel out. What formula that you used
Thank you for this video It was just so clear...I got it now.
Thank you!
I have one more question,
I am doing a RSA encryption problem. and I want to know how to solve bigger number modular without fast modulation.
For ex: 2015^17 mod (3233) how would I break down the number and exponentials?
@ImDHML: One way to start on a similar example: If we want 2018^19 (mod 3104), this would be congruent to (-1086)^19 (mod 3104), then it might help to write 1086 as 2x3x181, ...
Great video, but just one question(I'm dumb), as the result of x congruent 7(mod 29), wouldn't that means x-7=29k?(k is a random number that representing the times of 29), I'm kinda confused cuz the way you check the result is kinda like taking "x=7" instead of "x congruent 7"
If you have an answer of 7, then 7 plus or minus a multiple of 29 should work too
@@MathsWithJay Got to say I'm surprised by the fact that there's actually a reply for a video that existed for so long, I'm really grateful, ty!
excellent explaination...slow and steady
Thank you; it's good to know that you've found this useful.
Better than my cryptography textbook thanks so much!!
Wow, thanks!
so we were using euclids algorithm basically if the a and n are laege odd numbers?
or do you mean prime?
I was stuck with why the multiplication if x*n becomes just x, but now I understand why, I just couldn't see it because my professor thinks it's obvious matter. Thank you!
You're very welcome!
You just healed my headache
A new medication for headache?!
Yep! It's called "explaining complex concepts with few clear steps instead of throwing a bunch of formulas and hoping your students will figure it out". Altought, you can't find it in drug stores. It's quite rare...
Thank you!
OK. I am lost at the last step. How did you go from X is congruent to 36 (Mod29) to Xi s congruent to 7 (Mod29)? Please show steps when responding. Thank you.
36-29 = 7
Excellent explanation, the best on here by a long way.
Glad you think so!
thank you finally,
after hours of searching
Glad I could help
Thank you so much! I have been trapped on this for weeks..
Glad I could help!
how to solve the same equations in two variables.can we split the va riables in single variables equations.?
How would you do it for both negative solutions?
Do you have an example in mind?
Maths with Jay it doesn’t exactly have two negative solutions, but solving 5x congruent to 9mod8 gave me v = -3 and w = 2, so I’m a bit confused how to solve the last part (the part after we calculate v and w ) and how to check the answer if the v is negative
You could make v positive by adding on 8 because you are using mod 8. (You could also make the question simpler by subtracting 8 from 9) Both should give the same answer.
where did that +4 go at 8:51?
@expose3000: 5+4*5=(1+4)*5=5*5
@@MathsWithJay ah okay, thanks for the clarification! Excellent video
@@MathsWithJay is this something that is special for this case or do you always try to simplify it down like that
Thank you!
It is not a special case - it's what we always do
This is the only explanation of this that makes sense.
Thanks for letting us know.
What is the program that you write the equations
I love you! seriously you saved me
@Muhammad: Thank you!
very nice :) .. but what if i have something like 21x=11mod3
(by = i means to congruent)
so (21,3) dos not divide 1 .
but this linear congruent is a part of Chinese remainder theorem problem..
Do you really mean mod 3? If so, 21 is congruent to 0, and 11 is not, so there is no possible value for x.
What happen to the 4 during backwards induction? It just seemed to dissappear for no reason.
Where is the 4?
9:27, when it says "5-2x12+4x5"
Oh yes, I see where it is. What happens is that 5 + 4 x 5 = 5 x 5.
ah ok. understood thanks.
Outstanding video lecture.
Glad you liked it!
You are so helpful, Ma'am! Thank you!
@Jen, you are so welcome!
17x ≡ 3 mod 29 =>
-12x ≡ 3 mod 29
Now divide by 3 to get:
-4x ≡ 1 mod 29
What multiple of 29 must I add to 1 to get a multiple of 4?
29 mod 4 ≡ 1, so subtract 1 multiple of 29:
-4x ≡ -28 mod 29
Now divide by -4:
x ≡ 7 mod 29
The general solution is x = 7 + 29n.
Thank you for taking the time to respond to this example....it will be interesting to see other viewers' comments on this.
this does not work on every linear congruent right? I mean.... I tried the method yes, but I also used the "Linear Congruence Calculator" and they have different results, idk why and idk which is correct or not.
I have to do 13x+5=6x+15 (mod 20) anything special I have to do to deal with the integer addition?
I could have started with 20x + 1 ≡ 3x + 4, and then subtracted 3x and 1 from both sides. I could check the answer in 20x + 1 ≡ 3x + 4..and see that it works.
Nicely explained as usual
Thank you for your positive feedback.
when you said 17v is congruent to 1 (mod 29), is that true because 29 is prime, in other words if it was 17x is congruent to 3 (mod 30), would it still be correct to write 17v is congruent to 1 (mod 30)?
17v is congruent to 1 (mod 29) because we worked out that 17x12 - 7x29 = 1. If you want to use mod 30, you need to start at the beginning again, using 30 instead of 29.
where did the +4 go
@8:59
@Royce: It has been added to 1 to make 5 because 5 + 4 x 5 = 1 x 5 + 4 x 5 = 5 x 5
Same question, but now I think, since there is 5 + 4 × 5, we can write it as:
5 + 4(5)
=1(5) + 4(5)
=5 (1 + 4)
=5 (5)
or 5 × 5.
How did we leave with just only x at the last bit please rep thanks
@Ian: At what time in the video please
What if x is a negative number after the linear combination?
@magenta: Just add a multiple of 29 to make it positive
Maths with Jay makes sense thank you!!
Can also solve with 17x-3 = 29k. Try different values of k, i.e. 0,1,2,... until you get an integer solution for x. With k=4, then x=7. Much easier for small values of k. Otherwise, not practical without a computer.
Your video was amazing thank you very much! Just one quick question, let's say that in the end, the result was
x congruent 14 (mod 19). Would x be equal to 14 or 5 (as 19-14= 5 but it is not arranged in that order)?
Thank you for your feedback, Aimee. You can add or subtract multiples of 19 from 14, so the best answer is 14, but 14 - 19 = -5 is also an answer. 5 is not congruent to 14 (mod 19).
Great explanation
@Zeke Kwok: Thank you!
Thank you so much from Belgium
Thank you!
Thank you!! this was easy to follow. Great voice, patient.
@Patricia: Thank you so much!
You don't realize how big of a weight you just lifted off of my shoulders.
Thank you!
Thank you for posting this! very helpful :)
Many thanks for your feedback. It is really appreciated.
Well, it's an interesting algorithm, but intuitively, it doesn't feel right unless you have a grasp of the underlying arithmetic. Everybody should try at least once to solve the equivalent Diophantine equation by the usual method - you'll find that the amount of computation is the same, and you'll feel more confident with the Euclidean Algorithm.
In this case, we want to solve the Diophantine equation 17x = 29a + 3 where x, a are integers. We proceed by consecutive substitutions, each one of which is an integer. Notice how the denominator reduces in size at each step:
x = (29a+3)/17 = a + (12a+3)/17 then let b = (12a+3)/17 which must be an integer if x and a are integers as we require. Then we rearrange:
a = (17b-3)/12 = b + (5b-3)/12 then let c = (5b-3)/12
b = (12c+3)/5 = 2c + (2c+3)/5 then let d = (2c+3)/5
c = (5d-3)/2 = 2d - 1 + (d-1)/2 [_For the final step I'll use n as the integer (because e might cause confusion)_] then let n = (d-1)/2 which gives
d = 2n+1
Each consecutive integer n will then generate solutions.
So we can now substitute for d to get c in terms of n, then express b in terms of n, and a in terms of n and finally x in terms of n:
c = (5d-3)/2 = (5(2n+1)-3)/2 = 5n+1
b = (12(5n+1)+3)/5 = 12n+3
a = (17(12n+3)-3)/12 = 17n+4
x = (29(17n+4)+3)/17 = 29n+7
Notice how the arithmetic is equivalent to that presented when following Euclid's Algorithm in the video. The solutions are just the same and you can of course check by trying values of n from 0, 1, 2 ... etc. which will each generate a value for x that when multiplied by 17 and divided by 29 will leave a remainder of 3. Working through this kind of "primitive" method may well have been the basis for Euclid's insight into the deeper properties of congruence arithmetic.
Thank you for taking the time to give such a detailed response to this video
Excellent explanation, thank you!
Thank you very much!
How does 12 x 17x change to be just x in the last step?
We are rearranging the previous line where there was a 1 on the LHS.
How to solve linear congruence questions using maple software?
www.maplesoft.com/support/help/Maple/view.aspx?path=Task%2FSolveEqnModuloN
Should call it maths with bae
wow this really helped me get it! thanks!
@S L: Thank you!
Wow! God bless you. My class was moved to an online class due to COVID-19 and I have been struggling so much with this because nobody thoroughly explains it like you just did. Thank you so much.
Thank you very much Paula-Dee Cameron! It's great to know that this is still so useful!
You explain excellent
Glad you think so!
why didn't you just shift the inverse of 17 to the other side and take the modulo of it?
How come they didn't work for 2X is congruent to 3 (mod 5)
What do you get for v and x?
Wish youtube had a 3x button.😂. Great video though
@ANKIT BATCHALI: Thank you! Recent videos are faster.
Thank you! I finally understand this topic.
You are welcome!
thank you Maths with Jay
#Respect
Many thanks Reuben!
absolutely loved it
Thank you!
How 17v = 1 +- 29w??
And why we take -29?? Please respond
At what time in the video?
What happened to the 4 from 4x5?
@Haval Mohammed: At what time in the video?
@@MathsWithJay sorry I realized after what happened with it. But timestamp at 8:40. Thanks for a great explanation!
@Haval Mohammed: OK...Thank you!
What happened to 12 at 9.54?
We replace it by 29 - 17 from the top line
How we can show that 89 | 2^44 - 1 ????
Is that a congruence?
Thanks from saudi arabia
Greetings to Saudi Arabia from London
Bonjour,
Solving such equations are much more simply by the pattern of Ouragh . Indeed for the equation treated in the video this scheme is as following
.....29........17........12.........5.........2.........1
..................-1.........-1.........-2........-2
.................12.........-7..........5........-2.........1
and so we have x is congruent to 12 * 3 [ 29] is x = 7 [29]
Cordially.
very easy to understand thank you
@Fadhil Sugiharto: Excellent! Thank you!
Thank you (math with jay) 😓👍💯
@Eng Menghong: Thank you!
what if I had to solve 3x + 2 = 3 (mod 5)? I'm getting confused on + 2 part, Please help
@ImDHML: Start by subtracting 2 from both sides.
@@MathsWithJay does that mean it will be 3x = 3(mod 5) - 2 or 3x = 3 - 2(mod 5)? ty for replying
3 - 2, so 1 (mod 5)
Try putting a number in for x, so if x is 4 for example, 3x is congruent to 12, so congruent to 2 mod 5 and 3x + 2 would be congruent to 4, then you can see what happens when you add or subtract 2 from both sides
Good work.
Thanks! You may also like: ua-cam.com/video/zIFehsBHB8o/v-deo.html
Thank you!, excellent video
Glad it helped!
Thanks so much the explanation was on point ☺️
You’re welcome 😊
doing the matrix version of Euclid's algorithm will cut out having to do that back substitution part.
Thank you!!!! so much this was a really clear explanation.
Glad it was helpful!
How to get 896 mod29?
How to find mod of 3digits no
(This is not a linear congruence.)
Divide 896 by 29 and find the remainder.
Maths with Jay tqu😊