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Prove: If p is prime and p ≡ 7 (mod 8), then p | 2(p−1)/2 −...

Prove: If p is prime and p ≡ 7 (mod 8), then p | 2(p−1)/2 − 1. (Hint: Use the Legendre symbol (2/p) and Euler's criterion.)

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Here proof is p|(2^(p-1)/2-1) and not above you mentioned.the proof is below using Legendre symbol and Euler's criterion theorem .Thank you.

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