"Legendre symbol" meaning in English

{
  "etymology_text": "Named after French mathematician Adrien-Marie Legendre (1752–1833), who introduced the symbol in 1798 in his work Essai sur la Théorie des Nombres (\"Essay on the Theory of Numbers\").",
  "forms": [
    {
      "form": "Legendre symbols",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "args": {},
      "expansion": "Legendre symbol (plural Legendre symbols)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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          "name": "Number theory",
          "orig": "en:Number theory",
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      "examples": [
        {
          "text": "1994, James K. Strayer, Elementary Number Theory, Waveland Press, 2002, Reissue, page 109,\nOur only method at present for the computation of Legendre symbols requires a possible consideration of (p-1)/2 congruences (unless, of course, we are fortunate enough to encounter the desired quadratic residue along the way)."
        },
        {
          "ref": "2006, Neville Robbins, Beginning Number Theory, 2nd edition, Jones & Bartlett, page 195",
          "text": "The Jacobi symbol, which generalizes the Legendre symbol, sheds some additional light on how to determine whether (7.29) has solutions when m has two or more distinct prime factors.",
          "type": "quotation"
        },
        {
          "ref": "2013, Song Y. Yan, Number Theory for Computing, Springer, page 149",
          "text": "Jacobi symbols can be used to facilitate the calculation of Legendre symbols. In fact, Legendre symbols can be eventually calculated by Jacobi symbols [17]. That is, the Legendre symbol can be calculated as if it were a Jacobi symbol. For example, consider the Legendre symbol #x5C;left(#x5C;frac#x7B;335#x7D;#x7B;2999#x7D;#x5C;right) where 335 = 5·67 is not a prime (of course, 2999 is a prime, otherwise, it is not a Legendre symbol).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A mathematical function of an integer and a prime number, written (a/p), which indicates whether a is a quadratic residue modulo p."
      ],
      "id": "en-Legendre_symbol-en-noun-IrI3xqFA",
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          "number theory",
          "number theory"
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        [
          "integer",
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          "prime number",
          "prime number"
        ],
        [
          "quadratic residue",
          "quadratic residue"
        ],
        [
          "modulo",
          "modulo"
        ]
      ],
      "raw_glosses": [
        "(number theory) A mathematical function of an integer and a prime number, written (a/p), which indicates whether a is a quadratic residue modulo p."
      ],
      "related": [
        {
          "word": "Euler's criterion"
        },
        {
          "word": "Jacobi symbol"
        },
        {
          "word": "quadratic reciprocity"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Adrien-Marie Legendre",
        "Legendre symbol"
      ]
    }
  ],
  "word": "Legendre symbol"
}

{
  "etymology_text": "Named after French mathematician Adrien-Marie Legendre (1752–1833), who introduced the symbol in 1798 in his work Essai sur la Théorie des Nombres (\"Essay on the Theory of Numbers\").",
  "forms": [
    {
      "form": "Legendre symbols",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
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      "expansion": "Legendre symbol (plural Legendre symbols)",
      "name": "en-noun"
    }
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Euler's criterion"
    },
    {
      "word": "Jacobi symbol"
    },
    {
      "word": "quadratic reciprocity"
    }
  ],
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      "examples": [
        {
          "text": "1994, James K. Strayer, Elementary Number Theory, Waveland Press, 2002, Reissue, page 109,\nOur only method at present for the computation of Legendre symbols requires a possible consideration of (p-1)/2 congruences (unless, of course, we are fortunate enough to encounter the desired quadratic residue along the way)."
        },
        {
          "ref": "2006, Neville Robbins, Beginning Number Theory, 2nd edition, Jones & Bartlett, page 195",
          "text": "The Jacobi symbol, which generalizes the Legendre symbol, sheds some additional light on how to determine whether (7.29) has solutions when m has two or more distinct prime factors.",
          "type": "quotation"
        },
        {
          "ref": "2013, Song Y. Yan, Number Theory for Computing, Springer, page 149",
          "text": "Jacobi symbols can be used to facilitate the calculation of Legendre symbols. In fact, Legendre symbols can be eventually calculated by Jacobi symbols [17]. That is, the Legendre symbol can be calculated as if it were a Jacobi symbol. For example, consider the Legendre symbol #x5C;left(#x5C;frac#x7B;335#x7D;#x7B;2999#x7D;#x5C;right) where 335 = 5·67 is not a prime (of course, 2999 is a prime, otherwise, it is not a Legendre symbol).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A mathematical function of an integer and a prime number, written (a/p), which indicates whether a is a quadratic residue modulo p."
      ],
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "prime number",
          "prime number"
        ],
        [
          "quadratic residue",
          "quadratic residue"
        ],
        [
          "modulo",
          "modulo"
        ]
      ],
      "raw_glosses": [
        "(number theory) A mathematical function of an integer and a prime number, written (a/p), which indicates whether a is a quadratic residue modulo p."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Adrien-Marie Legendre",
        "Legendre symbol"
      ]
    }
  ],
  "word": "Legendre symbol"
}