Thread: congruence

a) If a^p = b^p mod p, prove that a = b mod p

b) If a a = b mod p, prove that a^p = b^p mod p

#1: (Hint: Fermat's theorem)

#2: You can use the fact that if and then . Then it's just a matter of considering and

Originally Posted by o_O

#1: (Hint: Fermat's theorem)

#2: You can use the fact that if and then . Then it's just a matter of considering and

trying to use fermats theorem but still cant prove it

Originally Posted by bigb

a) If a^p = b^p mod p, prove that a = b mod p

Do what o_O did.
Fermat's little theorem says and .
Therefore we can replace by and by since they are congruent.
This leaves us with .

Originally Posted by ThePerfectHacker

Do what o_O did.
Fermat's little theorem says and .
Therefore we can replace by and by since they are congruent.
This leaves us with .

Can anyone work this out.. really cant seem to solve this

Fermat's theorem:

Originally Posted by bigb

a) If a^p = b^p mod p, prove that a = b mod p

b) If a a = b mod p, prove that a^p = b^p mod p

I made a mistake in typing out the problem for part b if that makes a differnece...it should be a^p = b^p mod p, prove that a^P = b^p mod p^2