I just want to say thank you and that you have an excellent way of teaching. I learned more in this video than in my whole class and my final is tomorrow!
The title is misspelled, just a minor point. I am learning a lot, thanks. (Although I am watching on 2x or 3x speed most of the time. I personally think you can make the course slightly harder/faster/denser to make it more interesting!)
28:15 Why in the first form there is that additional requirement for `a` and `p` to be relatively prime, but there isn't such a requirement in the second form? Isn't it that the first form is just the second form divided by `a` on both sides? 54:15 3^5 mod 7 is 5, not 2. And yes, we did that before, so this mistake shouldn't have happened :P Especially that it lasted on the board for 7 minutes and nobody spotted the error :P And you even hovered the mouse cursor over it several times when drawing the box around that row. You also told that there shouldn't be any repetitions in this row, while there clearly were: the 2 repeated twice (because of the error). So there were multiple occasions to spot the error.
Answering 28:15 for u, actually it is the same thing. On theorem (2), if 'a' is divisible by 'p', namely a=kp for some positive integer k then we have a^p=(kp)^p=0(=p=kp)=a then whether 'a' is divisible by 'p' or not means nothing from the second theorem. however, on theorem (1), if 'a' is divisible by 'p', namely a=kp for some positive integer k then we have a^p=(kp)^p=0 =/=1 hence 'a' is not divisible by 'p' is important here
Thanks a lot for this, very informative. When you calculate the table of powers of a mod 7, am I right in thinking you can use (a mod n) x (b mod n) mod n = ab mod n as a shortcut to avoid using the calculator after you've calculated the first two columns?
When you showed how a table was constructed for powers of 'a' mod 7, there were two entries of '2' in a row you stated as being a primitive root. Was one of those supposed to be a '5' or was I misunderstanding what was meant by 'unique'?
I just want to say thank you and that you have an excellent way of teaching. I learned more in this video than in my whole class and my final is tomorrow!
The title is misspelled, just a minor point. I am learning a lot, thanks. (Although I am watching on 2x or 3x speed most of the time. I personally think you can make the course slightly harder/faster/denser to make it more interesting!)
Good lecture. Thanks a lot!:
28:15 Why in the first form there is that additional requirement for `a` and `p` to be relatively prime, but there isn't such a requirement in the second form? Isn't it that the first form is just the second form divided by `a` on both sides?
54:15 3^5 mod 7 is 5, not 2. And yes, we did that before, so this mistake shouldn't have happened :P Especially that it lasted on the board for 7 minutes and nobody spotted the error :P And you even hovered the mouse cursor over it several times when drawing the box around that row. You also told that there shouldn't be any repetitions in this row, while there clearly were: the 2 repeated twice (because of the error). So there were multiple occasions to spot the error.
Answering 28:15 for u, actually it is the same thing.
On theorem (2),
if 'a' is divisible by 'p', namely a=kp for some positive integer k
then we have a^p=(kp)^p=0(=p=kp)=a
then whether 'a' is divisible by 'p' or not means nothing from the second theorem.
however, on theorem (1),
if 'a' is divisible by 'p', namely a=kp for some positive integer k
then we have a^p=(kp)^p=0 =/=1
hence 'a' is not divisible by 'p' is important here
Thanks a lot for this, very informative. When you calculate the table of powers of a mod 7, am I right in thinking you can use (a mod n) x (b mod n) mod n = ab mod n as a shortcut to avoid using the calculator after you've calculated the first two columns?
+Michael Pound Yes, the laws of mod can be used to simplify calculations.
When you showed how a table was constructed for powers of 'a' mod 7, there were two entries of '2' in a row you stated as being a primitive root. Was one of those supposed to be a '5' or was I misunderstanding what was meant by 'unique'?
+Ray Howard You are correct, that is a mistake. With a = 3, a^5 = 243 and 243 mod 7 = 5. 3 IS a primitive root in mod 7.
Thanks for confirming. Also, thanks for the video.
Hello sir
On Euler theorem (2) say: "For positive integers a and n". Is the condition "co-prime" or "relatively prime" required? Or is it any a and n?
Hey if we wanna toeint of big value like 500 how can we find it??
thanks a lot for good advice to understood Euler theorem
bro.............you help me a lot many............infinite thanks love for you. Time [59:00- 1:01:00] is the best for me
outstanding!! thank you so much!
By this theorem, find out the total no. Of digit of 4697 to the power 789475 in 4 second ?
a^(phi(n)) mod n = a
Do "a" need to be smaller than "n"?
what about 3^7605%7=6
note that 7605=3 mod 7