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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