Euler's criterion

English

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

Euler's criterion

(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 ${\\displaystyle a^{(p-1)/2}}$ is congruent to 1 modulo p.

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

单词	Euler's criterion
释义	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 kɹaɪ̯.ˈtɪ.ɹi.ən/, /ˈɔɪ̯.lə(ɹ)z kɹɪ.ˈtɪ.ɹi.ən/ Proper noun Euler's criterion (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 ${\\displaystyle a^{(p-1)/2}}$ 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.
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