John D. Cook • 2/13/2026

Expressing a prime as the sum of two squares

The article discusses Fermat's theorem that an odd prime p can be expressed as the sum of two squares if and only if p ≡ 1 mod 4. It examines Gauss's elegant but computationally inefficient formula for finding such squares and contrasts it with Stan Wagon's more practical algorithm, which uses quadratic non-residues and the Euclidean algorithm for efficiency.

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#algorithm #number theory #modular arithmetic