John D. Cook • 2/14/2026

Finding a non-square mod p

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The article details Stan Wagon's algorithm for expressing a prime p ≡ 1 mod 4 as a sum of two squares, focusing on the first step: finding a quadratic non-residue (non-square) modulo p. It provides Python code using the Legendre symbol, discusses testing strategies using consecutive primes versus random candidates, and illustrates the process with large primes from cryptographic standards like Curve25519 and NIST P-384.

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#Python #cryptography #number theory
Finding a non-square mod p

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