Employ Fermat’s theorem to prove that, if p is an odd prime, then
(a) 1P−1 + 2p−1 + 3p−1 +⋯ + (p−1)p−1 ≡ −1 (mod p).
(b) 1p + 2p + 3p + ⋯ +(p−1)p ≡ 0 (mod p).
[Hint: Recall the identity 1 + 2 + 3 + ⋯ + (p−1) = p(p − l)/2.]
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