Abstract: Maple's routine testeq (written by Gaston Gonnet) is a probabilistic method for testing whether an expression is zero or not. It does this by putting in random numbers for variables and computing modulo a prime. E.g. > exp(2*x)*x*(x-1)-exp(x)^2*(x^2-x); 2 2 exp(2 x) x (x - 1) - exp(x) (x - x) > testeq(%); true I'll explain how testeq works and its limitations. Using some number theory I'll suggest some extensions that would make it possible for testeq to handle square roots and trigonometric functions properly.