Competition problem — Number theory

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Number theory Difficulty 5.6 AIME, harder Find the answer

11. Find the number of solutions to the congruence equation $x^{2} \equiv -1(\bmod m)$ (Hint: Use Exercise 6 of § 4 in Chapter 3, or use Corollary 3 of § 5 in this chapter).

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

None

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None

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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.