Another proof of the Two Squares Theorem via continuants
Barry R. Smith · arXiv (Cornell University) · 2013
Expressions involving continuants are given for the remainders when the Euclidean algorithm is performed with positive integers n and a for which $a^2 \equiv -1 \pmod{n}$. They give rise to a new proof that there is a pair of consecutive remainders whose squares sum to n and a generalization of this result to other pairs of remainders.