In number theory Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime. Precisely,
Let p be an odd prime and a an integer coprime to p. Then
Euler's criterion can be concisely reformulated using the Legendre symbol:
The criterion first appeared in a 1748 paper by Euler.
Famous quotes containing the word criterion:
“Faith in reason as a prime motor is no longer the criterion of the sound mind, any more than faith in the Bible is the criterion of righteous intention.”
—George Bernard Shaw (18561950)