Euler's criterion

English

Etymology

Named after Leonhard Euler (1707–1783), Swiss mathematician and physicist, who devised the criterion in 1748.

Pronunciation

• IPA^(key): /ˈɔɪ̯.lə(ɹ)z kɹaɪ̯ˈtɪ.ɹi.ən/, /ˈɔɪ̯.lə(ɹ)z kɹɪˈtɪ.ɹi.ən/

Proper noun

Euler's criterion

1. (number theory) A theorem which states that, given a positive integer a which is coprime to an odd prime number p, a is a quadratic residue of p if and only if $a^{(p-1)/2}$ is congruent to 1 modulo p.

Usage notes

• The calculation on the left side of the congruence — or the result thereof — can be denoted with the Legendre symbol.