Wilson's theorem WilsonsTheorem 2001-08-13 10:23:16 2008-05-17 20:12:40 Theorem \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} Wilson's theorem states that $$ (p-1)! \equiv -1 \pmod{p} $$ iff $p$ is prime (note that it must be positive).