Let a and b be integers not divisible by the prime number p. If a^p = b^p (mod p), prove that a^p = b^p (mod p^2).

Please help me!

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- Mar 28th 2007, 12:30 PMbluesilverCongruences modulo p
Let a and b be integers not divisible by the prime number p. If a^p = b^p (mod p), prove that a^p = b^p (mod p^2).

Please help me! - Mar 28th 2007, 08:25 PMThePerfectHacker
Okay, here is the proof below.

This example insipired me to create my own challenge.

**Theorem**If p does not divide a and b, such that,

a^p=b^p (mod p) then a^(p^2)=b^(p^2) (mod p^2).

Try to show that.