I'm looking for a quick way to find the solutions to the equation $n\equiv x^2\bmod p$ for prime $p$. Specifically, I'm interested in knowing all (or a large number of) the values of $p$ for a given value $n$. I know this work has been done before computers were invented - it used to be stored in big, thick textbooks, if memory serves. Does anybody know what I'm talking about, or is there no better way than to just put in the work myself?
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3https://www.jstor.org/stable/1967686?seq=2 – Jean Marie Apr 05 '22 at 18:24
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1If you want all solutions, you can find a primitive root and parametrize the quadratic residues as the powers of its square. Or you can just find all the squares of the numbers $1$ thru $(p-1)/2$. This can be done by computer to generate tables. – anon Apr 05 '22 at 18:31