"divisibility sequence" meaning in All languages combined

See divisibility sequence on Wiktionary

Noun [English]

Forms: divisibility sequences [plural]
Head templates: {{en-noun}} divisibility sequence (plural divisibility sequences)
  1. (number theory, algebra) Any sequence of integers {aₙ}, indexed by the natural numbers, such that if n is divisible by m then aₙ is divisible by aₘ. Wikipedia link: divisibility sequence Categories (topical): Algebra, Number theory Derived forms: strong divisibility sequence Translations (type of integer sequence): suite à divisibilité [feminine] (French), Teilbarkeitsfolge [feminine] (German), successione di divisibilità [feminine] (Italian)

Inflected forms

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        {
          "ref": "2012, P. Ingram, J. H. Silverman, “Primitive Divisors in Elliptic Divisibility Sequences”, in Dorian Goldfeld, Jay Jorgenson, Peter Jones, Dinakar Ramakrishnan, Kenneth Ribet, John Tate, editors, Number Theory, Analysis and Geometry, Springer,, page 244:",
          "text": "If #92;mathcalC#61;(C#95;n)#95;#123;n#92;ge 1#125; is any divisibility sequence, one says that a prime p is a primitive divisor of C#95;n if p#92;vertC#95;n but p#92;nmidC#95;1C#95;2C#95;#123;n-1#125;. Primitive divisors of certain divisibility sequences were studied by Zsigmondy [37] in the 19ᵗʰ century.",
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          "ref": "2013, Graham Everest, Thomas Ward, Heights of Polynomials and Entropy in Algebraic Dynamics, Springer, page 138:",
          "text": "These divisibility sequences satisfy the same recurrence relations as the polynomials #92;phi#95;n and #92;psi²#95;n (see Appendix C).",
          "type": "quote"
        },
        {
          "ref": "2021, Masum Billal, Samin Riasat, Integer Sequences, Springer, page 59:",
          "text": "Moreover, in order to keep a divisibility sequence normalized, we can assume without loss of generality that a#95;0 = 0 and a#95;1#61;1.",
          "type": "quote"
        }
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        "Any sequence of integers {aₙ}, indexed by the natural numbers, such that if n is divisible by m then aₙ is divisible by aₘ."
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        "(number theory, algebra) Any sequence of integers {aₙ}, indexed by the natural numbers, such that if n is divisible by m then aₙ is divisible by aₘ."
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      "translations": [
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          "code": "fr",
          "lang": "French",
          "sense": "type of integer sequence",
          "tags": [
            "feminine"
          ],
          "word": "suite à divisibilité"
        },
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          "code": "de",
          "lang": "German",
          "sense": "type of integer sequence",
          "tags": [
            "feminine"
          ],
          "word": "Teilbarkeitsfolge"
        },
        {
          "code": "it",
          "lang": "Italian",
          "sense": "type of integer sequence",
          "tags": [
            "feminine"
          ],
          "word": "successione di divisibilità"
        }
      ],
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  "word": "divisibility sequence"
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          "text": "If #92;mathcalC#61;(C#95;n)#95;#123;n#92;ge 1#125; is any divisibility sequence, one says that a prime p is a primitive divisor of C#95;n if p#92;vertC#95;n but p#92;nmidC#95;1C#95;2C#95;#123;n-1#125;. Primitive divisors of certain divisibility sequences were studied by Zsigmondy [37] in the 19ᵗʰ century.",
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        {
          "ref": "2021, Masum Billal, Samin Riasat, Integer Sequences, Springer, page 59:",
          "text": "Moreover, in order to keep a divisibility sequence normalized, we can assume without loss of generality that a#95;0 = 0 and a#95;1#61;1.",
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        "(number theory, algebra) Any sequence of integers {aₙ}, indexed by the natural numbers, such that if n is divisible by m then aₙ is divisible by aₘ."
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  "translations": [
    {
      "code": "fr",
      "lang": "French",
      "sense": "type of integer sequence",
      "tags": [
        "feminine"
      ],
      "word": "suite à divisibilité"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "type of integer sequence",
      "tags": [
        "feminine"
      ],
      "word": "Teilbarkeitsfolge"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "type of integer sequence",
      "tags": [
        "feminine"
      ],
      "word": "successione di divisibilità"
    }
  ],
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}

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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-02-26 from the enwiktionary dump dated 2025-02-21 using wiktextract (ce0be54 and f2e72e5). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

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