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).
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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.
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