The problem is actually slightly simpler than that, but I couldn't fit it all into the topic title.(adsbygoogle = window.adsbygoogle || []).push({});

Let p be a prime satisfying p = 5 (mod 8) and suppose that 'a' is a quadratic residue modulo p. I need to show that one of the values:

x = a^(p+3)/8 or x = 2a*(4a)^(p-5)/8

is a solution to the congruence x^2 = a (mod p).

I really have no idea how to even start this. If it was just a single case, I think I would be able to make some progress, but since I have to prove that one or the other works (depending on the situation), I'm totally lost. Any help is appreciated. Thanks!

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# Where does p = 5 (mod 8) solve x^2 = a?

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