JCSBimp's Hexagonal Orthogonal

Let m be an odd positive integer we wish to factor. Let c be the smallest integer (also positive) so that c²>m. (If m is a perfect square, we are done.) Set r=c²-m.

The least non-negative value of x for which x²+2cx+r is a perfect square is a value of x which produces s=c+x whose square differs from m by a perfect square amount t²: m=s²-t²=(s+t)(s-t), quite probably a desired factorization. (With hat-tip to Pierre de Fermat.)