@@aymenchamia7470 I do, and he is 100% right. Our lecturer is extremely smart and knowledgeable no doubt, but he just can’t explain the procedures and concepts in a simple enough way for anyone to understand.
It took you around 3 minutes to say what I needed to know, the same thing that my professor unsuccessfully tried to explain in one hour. Thank you so much
I wonder which professor took one hour for congruence 😅then for sure your whole syllabus time schedule gonna wasted..., ഒരു മയത്തിൽ ഒക്കെ ആവം കേട്ടോ ...
I am a senior math and CS major, I have used modulo almost as much as I’ve used pi and I have always been confused by congruency. No one has been able to explain congruency more clearly and digestible than you. Thank you!
30min trying to understand this congruence with my book . And this man make me understand it just in 1:46 seconds I wanna cry . Why professor make life complicated whyyy ... THANK YOU SO MUCH. I really respect you 🙏🙏
I watch 7 videos of about 20 minutes about modular arithmetic and didn’t understand anything but your 6 minutes video made me understand. I don’t know what to say
When I took abstract algebra, I found a ≡ b (mod n) quite confusing. The meaning seems to be a (mod n) = b (mod n), but equivalence must mean more than this.
@blackpenredpen Hi, when you say that 10 is congruent to 2 mod(4) but that cannot be according to the first definition because 10 and 2 doesn't have same remainders.Plz help
too late, but if by any chance someone needs it later on, this is one way to think about it. note that if you are dealing with mod(n), any integer will be congruent to the set starting from 0 to n-1(i.e: {0,1,2,...,n-1}), so for mod(4) we have {0,1,2,3}, so now what happens if we add "4" or multiples of it to any of these? well, u go a full cycle/s so 0+4 = 0 mod(4), 1 + 2*4 = 1 mod(4) etc. so essentially inside the realm of mod(4) adding 4 is analogous to adding 0 in the normal arithmetic, does not change a thing. so -2 mod(4) = -2+4 mod(4) = 2 mod(4).
@@Nour_Ayasrah when he says that 10 is congruent to 2 mod(4) but that cannot be according to the first definition because 10 and 2 does'nt have same remainders.Plz help
@@azharuddin7013 hey buddy, the first definition says that both numbers have the same remainder when divided by n, and that is true here. 2/4 = 0*4 + 2(this 2 here is the remainder) 10/4 = 2*4 + 2(again this is the remainder) since in both cases the remainder is 2, they are congruent
(by wikipaedia) Actually, the first claim is the most correct one, same remainder when a and b are divided by n, a = kn + r, b = jn + r then we have a - b = (k-j)n + 0 which means that n | a - b (the last claim). If we add b to both side, a = Kn + b by setting K = k - j. edit: depends on variables to choose the most suitable one.
In Beachy 4th Ed., the authors write " a ≡ b (mod n) if and only if n|(a - b)." The proof goes in both directions, so you see that n|(a -b) does indeed show that a/n and b/n have the same remainder. I just finished going over this proof again for my abstract algebra class. Very simple when you do the proof both ways.
1)PROBLEMA NIVEL UNI: TEMA: DIVISIBILIDAD a1b2c3d4=13° a2b3c4d^a2c=13°+3 a3c=7°+5 a2c --> mínimo calcule a+c 2)Calcule el residuo de dividir E entre 25 E=24^95 +24^94 .7+24^93 .7^2+24^92 .7^3+......+24.7^94 +7^95 3)halle el valor de "a": ( aa(b+3)3(a+1)4₁₈ ^aa(a+1) ^ (a-1)aa₅ ) -a =9° 4) nnmmnnmm....nnmm₇=......p3₅ .... calcule el máximo valor de x en: mpnnpm₁₂=.......x₇ 4) ARITMÉTICA-MÚLTIPLOS halle el máximo valor de d.c si se sabe que: 2abba^(b!-a!) =11°+9 ademas: (b-5)a3cd5=99°+33
Wow I wish I found this in my first year. It would've saved me hours of lengthy abstract examples and confusion. Why do universities make things so unnecessarily complicated sometimes 🙄.
In 10 cong 14 (mod 4)-->10=k*4+14, why is k=-1? I understand that practically 10=(-1*4)+14-->10=-4+14-->10=10, and this seems to be via Substituion, but it also seems arbitrary. That's ambiguous, unlike operating a number to both sides of an equation.
Well in India there's an exam called NMTC where you have to learn this as a part of syllabus when you're in grade 6. By the way I'm of grade 6 and I enjoy watching your calculus lectures
Hey hope you are doing alright just I wanna say that GOD loved the world so much he sent his only begotten son Jesus to die a brutal death for us so that we can have eternal life and we can all accept this amazing gift this by simply trusting in Jesus, confessing that GOD raised him from the dead, turning away from your sins and forming a relationship with GOD. :)
Can you show why 6^n always ends with 6 for natural n>0 with this theorem? Trying with that but can't really show it. I tried induction but not sure how induction works with congruence.
I can guarantee that most people will confuse the activity shown as comparable to developing a conceptual understanding of modular congruence. If he provided any sort of discovery in which one could find the relativity of discrete mathematics while performing the procedures of modular arithmetics then we could satisfy the looming problem of: When and where have I seen this before? Instead, as is the case of 'cutting corners', he stressed his strategic competency while disregarding the importance of the methodical alternatives represented. Those people whom hate maths or find the language nonsensical and deceptive do so because oftentimes someone who is still learning to teach the subject(s) denotes pertinent information yet fails to instruct on the basis of that which is the significance of an ontology; implying that, the concepts which are introduced can be conferred to the relevancy of an instantaneous appreciation by others. Per inference, everyone not exploring a career as a mathematician is ignoring the facts of exercises of the discipline. Why teach math while you are not becoming a mathematician?
in Viet Nam, I have learned a|b means a:b don't have any remainder. so it kindda make me confused when I read a English book have the notation a|b which is means b:a don't have any remainder.
This guy nailed it. However, you might like to think about congruence, blackpenredpen covered it. Clarifying and memorable. Now I can move onto some proofs that have been baffling me!
what if i have -660x ≡ 121mod143 how does that turn into 55 ≡ 121mod43 (the professor wrote -660 ≡ 55mod43 but i just cant wrap my head around if someone could please help i would be very grateful.... i have a very important exam coming up ) i mean i understand why -660≡55mod143 and why then we go to 55≡121mod143 BUT HOW THE HELL WAS I SUPPOSED TO COME UP WITH THE NUMBER 55 thats my point what is the thought process behind getting to the replacement of -660 with 55 how did we come up with 55....??????
Hey bro ! Maybe I’m the latest one for this video but I want you to solve a math problem Here it is! Prove that: 1•3•5•...•2013+2•4•6•....•2014 is a multiple of 2015 I hope you see my comment and solve it for me. Thank you !
![Why you didn't learn tetration in school[Tetration]](http://i.ytimg.com/vi/Ea1_1aVfwl4/mqdefault.jpg)
What donuts are those?
The heart attack kind of donuts.
I meant to ask where they are from
Heaven
Look like Krispy Kreme.
Kevin got it!!
Some teachers in universities: 2h lecture
blacklenredpen: 6minutes
Too right mate, plus we can repay bprp's videos as often as we like.
He is just explaining the procedure not the theory, origins or proof
@@aymenchamia7470
I do, and he is 100% right.
Our lecturer is extremely smart and knowledgeable no doubt, but he just can’t explain the procedures and concepts in a simple enough way for anyone to understand.
It took you around 3 minutes to say what I needed to know, the same thing that my professor unsuccessfully tried to explain in one hour. Thank you so much
same
so fucking dmn right
True
True. I am right now going through the same experience.
I wonder which professor took one hour for congruence 😅then for sure your whole syllabus time schedule gonna wasted..., ഒരു മയത്തിൽ ഒക്കെ ആവം കേട്ടോ ...
Why is this video 2Pi minutes long ?
It's Tau
Burn!
2π=6
@@ansper1905 😑😑😑3.14159265358979323846264338
...
In can not be 3😐
@@sieger358 tell that to engineers
I am a senior math and CS major, I have used modulo almost as much as I’ve used pi and I have always been confused by congruency. No one has been able to explain congruency more clearly and digestible than you. Thank you!
Basically you throw out the quotient and keep the remainder. It's periodic math like the roots of a trig function.
PLEASE MORE MODULAR ARITHMETIC! You're the best
Sergio H will do!!
30min trying to understand this congruence with my book .
And this man make me understand it just in 1:46 seconds
I wanna cry .
Why professor make life complicated whyyy ...
THANK YOU SO MUCH.
I really respect you 🙏🙏
You should do more number theory, especially stuff like Euler’s totient function (since it’s my favorite subject ;D)!
I will. In the meantime, you can check out Max's videos here: ua-cam.com/channels/P-ZCMz7olJPUI78b_bQrvQ.htmlvideos?disable_polymer=1
Ahah, "killing all math":DDD
Eightc yup!!!!
And max, you can record an intro and send it to me via google drive so I can put it in my videos to let more ppl know about ur channel.
blackpenredpen thanks!!
I watch 7 videos of about 20 minutes about modular arithmetic and didn’t understand anything but your 6 minutes video made me understand. I don’t know what to say
Omg saving my grade once again. God bless you. Wish you had a patreon...
For those of you watching this in the future:
He does!
www.patreon.com/blackpenredpen
I learned more from this guy than from my entire math class xDDD
My math teacher made this look like rocket science...
same hahahahahahahhaha
When I took abstract algebra, I found
a ≡ b (mod n) quite confusing. The meaning seems to be
a (mod n) = b (mod n), but equivalence must mean more than this.
What the heck are you holding? A microphone? It looks like a psionic amplifier from the game System Shock 2. lol
*T H E R M A L D E T O N A T O R*
Poke ball
Your ability to change the marker you’re writing with so fast is amazing...
I read this comment and watched the video again just because of this. lmao. Wow! You were not joking.
@blackpenredpen Hi,
when you say that 10 is congruent to 2 mod(4) but that cannot be according to the first definition because 10 and 2 doesn't have same remainders.Plz help
Actually, they do. 10 divided by 4 is 2 with a remainder of 2. 2 divided by 4 is zero with a remainder of 2. Hope this helps.
im doing proofs with modular congruence and my head is exploding
do you have my schedule or something ?? how do you always upload what I need. thanks man !
OH wow!! ; )
H times i factorial
Algy Cuber Hi!!
PI(hi)
Nice
How a and b have same remainder ?(at 0:55)
: D this is exactly what I taught my students.
: )))))
Hey, good video! Could you explain how 10 ≡ -2 became 10 ≡ 2 by adding 4 to the -2?
I also want to know
too late, but if by any chance someone needs it later on, this is one way to think about it.
note that if you are dealing with mod(n), any integer will be congruent to the set starting from 0 to n-1(i.e: {0,1,2,...,n-1}), so for mod(4) we have {0,1,2,3}, so now what happens if we add "4" or multiples of it to any of these? well, u go a full cycle/s so 0+4 = 0 mod(4), 1 + 2*4 = 1 mod(4) etc.
so essentially inside the realm of mod(4) adding 4 is analogous to adding 0 in the normal arithmetic, does not change a thing. so -2 mod(4) = -2+4 mod(4) = 2 mod(4).
@@Nour_Ayasrah when he says that 10 is congruent to 2 mod(4) but that cannot be according to the first definition because 10 and 2 does'nt have same remainders.Plz help
@@azharuddin7013 hey buddy, the first definition says that both numbers have the same remainder when divided by n, and that is true here.
2/4 = 0*4 + 2(this 2 here is the remainder)
10/4 = 2*4 + 2(again this is the remainder)
since in both cases the remainder is 2, they are congruent
(by wikipaedia) Actually, the first claim is the most correct one, same remainder when a and b are divided by n,
a = kn + r, b = jn + r then we have a - b = (k-j)n + 0 which means that n | a - b (the last claim). If we add b to both side,
a = Kn + b by setting K = k - j.
edit: depends on variables to choose the most suitable one.
bro you really came through i was having trouble understanding that claim
So confused someone help! For 1) he says remainder is 2 and for 2) he says k=-1 which is the real answer
This is by far the best explanation....IMO!...here I come....!!!!
thanks!
I just keeping learning a lot from you.
Greetings from Mexico!
Can you talk about set theory or keep doing number theory?
Silvestre Frijol Cruz thank you!! I will focus on number theory, probability and combinatorics and calc.
*laughs in blue pen and green pen*
Are you a singaporean?
thankyou so much!! this really helped a lot 🥰🥰
In Beachy 4th Ed., the authors write " a ≡ b (mod n) if and only if n|(a - b)." The proof goes in both directions, so you see that n|(a -b) does indeed show that a/n and b/n have the same remainder. I just finished going over this proof again for my abstract algebra class. Very simple when you do the proof both ways.
THANK YOUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUUU!
P.S. I laughed when you said mod 1 kills all the math lol
I’m in knowledge bowl and this gave me a hard time
Please keep uploading Number Theory videos!
ok!!!!!!!!
1)PROBLEMA NIVEL UNI:
TEMA: DIVISIBILIDAD
a1b2c3d4=13°
a2b3c4d^a2c=13°+3
a3c=7°+5
a2c --> mínimo
calcule a+c
2)Calcule el residuo de dividir E entre 25
E=24^95 +24^94 .7+24^93 .7^2+24^92 .7^3+......+24.7^94 +7^95
3)halle el valor de "a":
( aa(b+3)3(a+1)4₁₈ ^aa(a+1) ^ (a-1)aa₅ ) -a =9°
4) nnmmnnmm....nnmm₇=......p3₅
....
calcule el máximo valor de x en:
mpnnpm₁₂=.......x₇
4) ARITMÉTICA-MÚLTIPLOS
halle el máximo valor de d.c si se sabe que:
2abba^(b!-a!) =11°+9 ademas: (b-5)a3cd5=99°+33
Wow I wish I found this in my first year. It would've saved me hours of lengthy abstract examples and confusion. Why do universities make things so unnecessarily complicated sometimes 🙄.
If n=1,a should be = to b right??
*kills all math*
very nice movie from Japan!
Thanks blackpenredpen for teaching us this!
"Do not do mod1" me: does mod 1
x(mod 1)=sawtooth[x]
TimE FOR COMPLEX MODS!
just had a great and clear understanding this was the lecture i needed thanks a lot mate!!!
Basic? Basic! yeah right - |: |:
Thanks a lot from Bangladesh
Our major instructor discussed this topic like using speed of light.... Boom finish!!
our instructor doesnt discuss to us hahahahahaha boom
Great video as always !
Helpful man thanks ; )
I have a doubt.
From a=(k×n)+b
Can we say this is similar to
dividend =divisor × quotient +remainder
Very helpful! Thanks!!
This video has the most epic donut-math intro to be honest.
كتبت كذا شجضنيريكثنرثكلهبنب وطلع لي هذا الفيديو 😂
Thanks man I was bit confused in equivalence relations when this came up , turns out I was interpreting it in a wrong way
I would attend every class of this guy 😭👍💓
The black ball looks like a prop from the movie parallel. Great explanation, weird microphone.
Thank you so mucj for this video! I was just watching an IMO prpblem solving video and i couldn't help but wonder what "mod(n)" meant.
OMG.. this vedio is about 2π min. Long
How could you formulate into words the question 28x ≡ 124 (mod 116)?
I have a hard time getting my head round what it means...
Dude i normally watch ur vids for fun but now i actually need help and i come back to ur channel😂
In 10 cong 14 (mod 4)-->10=k*4+14, why is k=-1?
I understand that practically 10=(-1*4)+14-->10=-4+14-->10=10, and this seems to be via Substituion, but it also seems arbitrary.
That's ambiguous, unlike operating a number to both sides of an equation.
A 4:28, you haven't convinced me : 10 and -2 when divided by 4 don't have the same remainder (you get 2 for 10 and -2 for -2).
blacklenredpen:"mod 1 kills everything, don't do that"
me:Wait why? lemme think, 3 mod 1 is.. oh is 0, ok, and 4 mod 1 is... Oh... I get it...
thaaaaaaaaaaaaank you , amazing , I love your explanation
C# exercises led me here... and I ain't even mad. Awesome video!
I spent an hour trying to understand it from my book... 6 minute video is what i needed.
Well in India there's an exam called NMTC where you have to learn this as a part of syllabus when you're in grade 6. By the way I'm of grade 6 and I enjoy watching your calculus lectures
how old is grade 6
Hey hope you are doing alright just I wanna say that
GOD loved the world so much he sent his only begotten
son Jesus to die a brutal death for us so that we can have eternal life and we can all accept this amazing gift this by simply trusting in Jesus, confessing that GOD raised him from the dead, turning away from your sins and forming a relationship with GOD. :)
Can you show why 6^n always ends with 6 for natural n>0 with this theorem? Trying with that but can't really show it. I tried induction but not sure how induction works with congruence.
hey man how did you derive the 2 equation i am having a lot of trouble understanding that . how did you remove mod from the equvalence and all that
Chinese ho Kya
Bro explained everything when my professor couldnt
I can guarantee that most people will confuse the activity shown as comparable to developing a conceptual understanding of modular congruence. If he provided any sort of discovery in which one could find the relativity of discrete mathematics while performing the procedures of modular arithmetics then we could satisfy the looming problem of: When and where have I seen this before? Instead, as is the case of 'cutting corners', he stressed his strategic competency while disregarding the importance of the methodical alternatives represented. Those people whom hate maths or find the language nonsensical and deceptive do so because oftentimes someone who is still learning to teach the subject(s) denotes pertinent information yet fails to instruct on the basis of that which is the significance of an ontology; implying that, the concepts which are introduced can be conferred to the relevancy of an instantaneous appreciation by others. Per inference, everyone not exploring a career as a mathematician is ignoring the facts of exercises of the discipline. Why teach math while you are not becoming a mathematician?
Eres un crack! Y todo lo digo en español, porque hasta en Latinoamerica disfrutamos de tus videos; en serio, aprendo muchísimo! Thank you!
I don't understand the third approach. What are we actually looking for?? Please answer thanks
I hope this comment will be noticed. Can b be greater than the value of n? Thank you in advance to the person who will answer✨✨
in Viet Nam, I have learned a|b means a:b don't have any remainder. so it kindda make me confused when I read a English book have the notation a|b which is means b:a don't have any remainder.
Excelente me salvaste de leer mucha álgebra, continua con el álgebra moderna que es bien interesante al igual que el calculo
I just wanna get a clean pause before the big damn THATSIT shows up
m² = m mod 1000
What could be the values of m??
Mom I'm becoming a mathematician
Lol
Great video, loving all the number theory :)
Thanks!!!
Why don't you use coler mike ,don't your hand get hurt while taching and holding mike continuesly 🤔
That’s so confusing ,this should be reported
This is not mathematically right. The congruence of a is the remainder that we get by devision to n
Why are you holding a bowling ball with a wire attached while using a marker and whiteboard...?
How 10 / 4 = 2 remainder 2 happened?? it should be remainder 5
you saved my exam tomorrow..thank you
Great Explaination sir 👍
11 grade student fom India
Can I solve for i in this equation?
(n-i) % (m+1) = 0
How a nd b same remainder when divided by b???plzzz reply..
summary: a = b mod m is known ads congrunce relation where a divides m and b divides m with same remainder and a is some constant times *m +b
Hi;
why/
4 mod 5 = -1
and
-1 mod 5=4
thanks
That is a weird-looking microphone!
Can you make it clear about the -ve 2 part....😅
This guy nailed it. However, you might like to think about congruence, blackpenredpen covered it. Clarifying and memorable. Now I can move onto some proofs that have been baffling me!
I want more video about this please
Great video, would love some more examples to cement how to use :)
For programmers, it simply means: a%n==b%n
what if i have -660x ≡ 121mod143 how does that turn into 55 ≡ 121mod43 (the professor wrote -660 ≡ 55mod43 but i just cant wrap my head around if someone could please help i would be very grateful.... i have a very important exam coming up )
i mean i understand why -660≡55mod143 and why then we go to 55≡121mod143 BUT HOW THE HELL WAS I SUPPOSED TO COME UP WITH THE NUMBER 55 thats my point what is the thought process behind getting to the replacement of -660 with 55 how did we come up with 55....??????
I’m in grade 8 and learning about modular arithmetic what am I doing lol
Thank you for explaining this in a straightforward manner, I FUCKING LOVE YOU!
Aren't they tasty 🍩 Donut?
best donuts, imo
Hey bro ! Maybe I’m the latest one for this video but I want you to solve a math problem
Here it is!
Prove that: 1•3•5•...•2013+2•4•6•....•2014 is a multiple of 2015
I hope you see my comment and solve it for me. Thank you !
a=b mod 1
Mathimatics end😎😎😎😎