Assuming that a and b are integers not divisible by the prime p, establish the following:
(a) If ap ≡ bp (mod p), then a≡b (mod p).
(b) If ap ≡ bp (mod p), then ap ≡ bp (mod p2).
[Hint: By (a), a = b + pk for some k, so that ap − bp = (b + pk)p−bp; now show that p2 divides the latter expression.]
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