"Euler's criterion" meaning in All languages combined

{
  "etymology_text": "Named after Leonhard Euler (1707–1783), Swiss mathematician and physicist, who devised the criterion in 1748.",
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      "args": {},
      "expansion": "Euler's criterion",
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  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
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          "name": "English entries with incorrect language header",
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
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      "glosses": [
        "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."
      ],
      "id": "en-Euler's_criterion-en-name-Px6Nydnf",
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "coprime",
          "coprime"
        ],
        [
          "quadratic residue",
          "quadratic residue"
        ],
        [
          "if and only if",
          "if and only if"
        ],
        [
          "congruent",
          "congruent"
        ],
        [
          "modulo",
          "modulo"
        ]
      ],
      "raw_glosses": [
        "(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."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Euler's criterion",
        "Leonhard Euler"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ˈɔɪ̯.lə(ɹ)z kɹaɪ̯.ˈtɪ.ɹi.ən/"
    },
    {
      "ipa": "/ˈɔɪ̯.lə(ɹ)z kɹɪ.ˈtɪ.ɹi.ən/"
    }
  ],
  "word": "Euler's criterion"
}

{
  "etymology_text": "Named after Leonhard Euler (1707–1783), Swiss mathematician and physicist, who devised the criterion in 1748.",
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        "en:Number theory"
      ],
      "glosses": [
        "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."
      ],
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "coprime",
          "coprime"
        ],
        [
          "quadratic residue",
          "quadratic residue"
        ],
        [
          "if and only if",
          "if and only if"
        ],
        [
          "congruent",
          "congruent"
        ],
        [
          "modulo",
          "modulo"
        ]
      ],
      "raw_glosses": [
        "(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."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Euler's criterion",
        "Leonhard Euler"
      ]
    }
  ],
  "sounds": [
    {
      "ipa": "/ˈɔɪ̯.lə(ɹ)z kɹaɪ̯.ˈtɪ.ɹi.ən/"
    },
    {
      "ipa": "/ˈɔɪ̯.lə(ɹ)z kɹɪ.ˈtɪ.ɹi.ən/"
    }
  ],
  "word": "Euler's criterion"
}