 Elliptic curve method

Attempt scalar multiplication on an elliptic curve modulo a composite integer. An addition denominator that is not invertible yields a greatest common divisor with the modulus; a value strictly between one and the modulus is a factor. The method exploits different orders of the reduced point at the unknown prime factors. For $y^2=x^3+5x-5$ modulo $221$, doubling $(1,1)$ gives $(14,-53)$; adding the original point requires division by thirteen, revealing $221=13\cdot 17$.