Euler's criterion

/ˈɔɪ̯.lə(ɹ)z kɹaɪ̯ˈtɪ.ɹi.ən//ˈɔɪ̯.lə(ɹ)z kɹɪˈtɪ.ɹi.ən/

proper noun

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.

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Meanings

proper noun
  1. mathematicsA 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.

Origin

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

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Cite this entry
APA

Euler's criterion. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Euler's%20criterion

MLA

“Euler's criterion.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Euler's%20criterion. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Euler's criterion,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Euler's%20criterion.

Source: Euler's criterion on Wiktionary, CC BY-SA 4.0.