A natural number p > 1 is prime if and only if (p − 1)! ≡ −1 (mod p). Stated by Wilson 1770, first proved by Lagrange 1771. Proof: pair each element of (Z/pZ)* with its multiplicative inverse; only ±1 are self-inverse, so all other…
A natural number p > 1 is prime if and only if (p − 1)! ≡ −1 (mod p). Stated by Wilson 1770, first proved by Lagrange 1771. Proof: pair each element of (Z/pZ)* with its multiplicative inverse; only ±1 are self-inverse, so all other…