Hi,

The problem is the following:

p an odd prime, a an integer, n≥2

Show: a^p≡1 (mod p^n) iff a≡1 (mod p^(n-1))

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I started by the following, but it gave me nothing

a^p≡1 (mod p^n)

a^p-1≡0 (mod p^n)

(a-1)(a^(p-1)+...+1)≡0 (mod p^n)

?

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