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Euler's criterion

/ˈɔɪ̯.lə(ɹ)z kɹaɪ̯ˈtɪ.ɹi.ən/

Euler's criterion 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.

Proper noun

Euler's criterion

  1. 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.

Origin of Euler's criterion

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

Questions about Euler's criterion

What does Euler's criterion mean?
Euler's criterion means 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.
What part of speech is Euler's criterion?
Euler's criterion is a proper noun.
How do you pronounce Euler's criterion?
Euler's criterion is pronounced /ˈɔɪ̯.lə(ɹ)z kɹaɪ̯ˈtɪ.ɹi.ən/.

Words near Euler's criterion in the dictionary

  1. Euler line
  2. Euler lines
  3. Euler method
  4. Euler spiral
  5. Euler's continued fraction formula
  6. Euler's criterion
  7. Euler's formula
  8. Euler's identity
  9. Euler's method
  10. Euler's number
  11. Euler's polyhedron formula

Source and license

Adapted from Wiktionary: Euler's criterion (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

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