Competition problem — Number theory

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Number theory Difficulty 5.9 AIME, harder Prove it

11. If the prime $p \equiv 5(\bmod 8)$ , then the congruence equation $x^{4} \equiv-1(\bmod p)$ has no solution.

Solution

11. See question 6.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.