Euler's Criterion is a formula for determining whether an integer is a quadratic residue modulo an odd prime: for a prime p and an integer a coprime to p, a raised to the power of half of p minus one is congruent to one modulo p exactly when some integer squared is congruent to a modulo p, and congruent to negative one modulo p otherwise. The criterion can be restated concisely using the Legendre symbol, and it dates from a 1748 paper by Leonhard Euler.
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StatementA formula for determining whether an integer is a quadratic residue modulo a prime. 1 Classification
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Source Euler's criterion (Wikipedia)
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1. Euler's criterion (Wikipedia)
Intro, sentence 1
Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime
Intro, sentence after the Legendre symbol reformulation
The criterion dates from a 1748 paper by Leonhard Euler.
In Branch: Number Theory, Lead sentence
In number theory, Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime.
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