How do I find quadratic residues mod n where n is not prime?

Asked Aug 12 '24 at 15:31

Active Aug 13 '24 at 01:37

Viewed 33 times

In particular, the N’s I am looking at are multiples of 2.

Given A and N, is there a non-iterative method to identify whether or not there exists a B such that B*B = A mod N?

I know with odd A I would only need to investigate odd B values (inverse for even A) and since A^2 == (N-A)^2 (mod N) I would only need to iterate up to N/2, but is that the best I can realistically do?

Note: this is not a duplicate as Eulers criterion only seems to only work for modulo primes, whereas I am asking for modulo a multiple of 2, which is not prime

edited Aug 13 '24 at 01:37

asked Aug 12 '24 at 15:31

Semi-Noob117

Take a tour. Learn more about asking questions. Moreover, try adding latex to it. – M.Riyan Aug 12 '24 at 15:42
https://en.wikipedia.org/wiki/Quadratic_residue#Composite_modulus_not_a_prime_power – CyclotomicField Aug 12 '24 at 17:38
@CyclotomicField so basically to identify if it’s a residue I would need to factor n, which is another huge problem in itself – Semi-Noob117 Aug 13 '24 at 01:41

How do I find quadratic residues mod n where n is not prime?

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