I know that if n is odd and has k distinct prime factors, then the number of roots, x^2 = 1 (mod n), is equal to 2^k.(adsbygoogle = window.adsbygoogle || []).push({});

However, I don't know how to give a formal proof to it.

I simply want to bypass the generalized form x^2 = a (mod n).

How can I prove it directly?

Thank you.

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# Square root of 1 with mod how to prove it?

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