"modular arithmetic" meaning in English

{
  "forms": [
    {
      "form": "modular arithmetics",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "modular arithmetic (countable and uncountable, plural modular arithmetics)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1969, Joseph Landin, An Introduction to Algebraic Structures, Dover, page 153",
          "text": "The reader now has examined, in some detail, several specific modular arithmetics, namely, #x5C;mathbb#x7B;Z#x7D;#x5F;2,#x5C;mathbb#x7B;Z#x7D;#x5F;5,#x5C;mathbb#x7B;Z#x7D;#x5F;6,#x5C;mathbb#x7B;Z#x7D;#x5F;7,#x5C;mathbb#x7B;Z#x7D;#x5F;8 and #x5C;mathbb#x7B;Z#x7D;#x5F;9.",
          "type": "quotation"
        },
        {
          "ref": "2010, Christof Paar, Jan Pelzl, Understanding Cryptography: A Textbook for Students and Practitioners, Springer, page 13",
          "text": "In this section we use two historical ciphers to introduce modular arithmetic with integers. Even though the historical ciphers are no longer relevant, modular arithmetic is extremely important in modern cryptography, especially for asymmetric algorithms.",
          "type": "quotation"
        },
        {
          "ref": "1997, Robert E. Jamison, “Rhythm and Pattern: Discrete Mathematics with an Artistic Connection for Elementary School Teachers”, in Joseph G. Rosenstein, Deborah S. Franzblau, Fred S. Roberts, editors, Discrete Mathematics in the Schools, American Mathematical Society, page 215",
          "text": "Hence for prime moduli, modular arithmetic is very similar to regular rational arithmetic with all four operations defined.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any system of arithmetic for integers which, for some given positive integer n, is equivalent to the set of integers being mapped onto the finite set {0, ... n} according to congruence modulo n, and in which addition and multiplication are defined consistently with the results of ordinary arithmetic being so mapped."
      ],
      "id": "en-modular_arithmetic-en-noun-4IWSB3ws",
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "arithmetic",
          "arithmetic"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "set",
          "set"
        ],
        [
          "congruence",
          "congruence"
        ],
        [
          "modulo",
          "modulo"
        ],
        [
          "addition",
          "addition"
        ],
        [
          "multiplication",
          "multiplication"
        ]
      ],
      "raw_glosses": [
        "(number theory) Any system of arithmetic for integers which, for some given positive integer n, is equivalent to the set of integers being mapped onto the finite set {0, ... n} according to congruence modulo n, and in which addition and multiplication are defined consistently with the results of ordinary arithmetic being so mapped."
      ],
      "related": [
        {
          "word": "modulo"
        }
      ],
      "synonyms": [
        {
          "sense": "system of finite arithmetic",
          "word": "clock arithmetic"
        }
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "system of finite arithmetic",
          "word": "modulaariaritmetiikka"
        },
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "system of finite arithmetic",
          "word": "modulaarinen aritmetiikka"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "system of finite arithmetic",
          "tags": [
            "feminine"
          ],
          "word": "aritmetica modulare"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "system of finite arithmetic",
          "tags": [
            "feminine"
          ],
          "word": "aritmetica dell'orologio"
        }
      ],
      "wikipedia": [
        "modular arithmetic"
      ]
    }
  ],
  "word": "modular arithmetic"
}

{
  "forms": [
    {
      "form": "modular arithmetics",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "~"
      },
      "expansion": "modular arithmetic (countable and uncountable, plural modular arithmetics)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "modulo"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "English uncountable nouns",
        "en:Number theory"
      ],
      "examples": [
        {
          "ref": "1969, Joseph Landin, An Introduction to Algebraic Structures, Dover, page 153",
          "text": "The reader now has examined, in some detail, several specific modular arithmetics, namely, #x5C;mathbb#x7B;Z#x7D;#x5F;2,#x5C;mathbb#x7B;Z#x7D;#x5F;5,#x5C;mathbb#x7B;Z#x7D;#x5F;6,#x5C;mathbb#x7B;Z#x7D;#x5F;7,#x5C;mathbb#x7B;Z#x7D;#x5F;8 and #x5C;mathbb#x7B;Z#x7D;#x5F;9.",
          "type": "quotation"
        },
        {
          "ref": "2010, Christof Paar, Jan Pelzl, Understanding Cryptography: A Textbook for Students and Practitioners, Springer, page 13",
          "text": "In this section we use two historical ciphers to introduce modular arithmetic with integers. Even though the historical ciphers are no longer relevant, modular arithmetic is extremely important in modern cryptography, especially for asymmetric algorithms.",
          "type": "quotation"
        },
        {
          "ref": "1997, Robert E. Jamison, “Rhythm and Pattern: Discrete Mathematics with an Artistic Connection for Elementary School Teachers”, in Joseph G. Rosenstein, Deborah S. Franzblau, Fred S. Roberts, editors, Discrete Mathematics in the Schools, American Mathematical Society, page 215",
          "text": "Hence for prime moduli, modular arithmetic is very similar to regular rational arithmetic with all four operations defined.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any system of arithmetic for integers which, for some given positive integer n, is equivalent to the set of integers being mapped onto the finite set {0, ... n} according to congruence modulo n, and in which addition and multiplication are defined consistently with the results of ordinary arithmetic being so mapped."
      ],
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "arithmetic",
          "arithmetic"
        ],
        [
          "integer",
          "integer"
        ],
        [
          "set",
          "set"
        ],
        [
          "congruence",
          "congruence"
        ],
        [
          "modulo",
          "modulo"
        ],
        [
          "addition",
          "addition"
        ],
        [
          "multiplication",
          "multiplication"
        ]
      ],
      "raw_glosses": [
        "(number theory) Any system of arithmetic for integers which, for some given positive integer n, is equivalent to the set of integers being mapped onto the finite set {0, ... n} according to congruence modulo n, and in which addition and multiplication are defined consistently with the results of ordinary arithmetic being so mapped."
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "modular arithmetic"
      ]
    }
  ],
  "synonyms": [
    {
      "sense": "system of finite arithmetic",
      "word": "clock arithmetic"
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "system of finite arithmetic",
      "word": "modulaariaritmetiikka"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "system of finite arithmetic",
      "word": "modulaarinen aritmetiikka"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "system of finite arithmetic",
      "tags": [
        "feminine"
      ],
      "word": "aritmetica modulare"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "system of finite arithmetic",
      "tags": [
        "feminine"
      ],
      "word": "aritmetica dell'orologio"
    }
  ],
  "word": "modular arithmetic"
}