Prove that if p is an odd prime, then x 2 ≡ 2 (mod p) has solutions if and only if p ≡ 1 or 7 (mod 8).
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Step 1
Step 1: Recall the problem statement: We need to prove that if \( p \) is an odd prime, then the congruence \( x^2 \equiv 2 \pmod{p} \) has solutions if and only if \( p \equiv 1 \) or \( 7 \pmod{8} \). Show more…
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