"rank of apparition" meaning in All languages combined

See rank of apparition on Wiktionary

Noun [English]

Forms: ranks of apparition [plural]
Head templates: {{en-noun|ranks of apparition}} rank of apparition (plural ranks of apparition)
  1. (number theory) Given a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m; Categories (topical): Number theory Synonyms: Fibonacci entry point (english: for the [[Fibonacci sequence]])
    Sense id: en-rank_of_apparition-en-noun-GYq4MvYu Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 50 50 Disambiguation of Entries with translation boxes: 51 49 Disambiguation of Pages with 1 entry: 51 49 Disambiguation of Pages with entries: 52 48 Topics: mathematics, number-theory, sciences
  2. (number theory) Given a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m; Categories (topical): Number theory Synonyms: Fibonacci entry point (english: for the [[Fibonacci sequence]])
    Sense id: en-rank_of_apparition-en-noun-bamKCdUQ Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 50 50 Disambiguation of Entries with translation boxes: 51 49 Disambiguation of Pages with 1 entry: 51 49 Disambiguation of Pages with entries: 52 48 Topics: mathematics, number-theory, sciences

Inflected forms

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          "ref": "1986, Joseph H. Silverman, The Arithmetic of Elliptic Curves, Springer, page 114:",
          "text": "Let (W#x5F;n) be an EDS^([Elliptic Divisibility Sequence]) associated to an elliptic curve E#x2F;K and a nonzero point P#x5C;inE(K) of finite order. Let r#x5C;ge 2 be the smallest index such that W#x5F;r#x3D;0. (The number r is called the rank of apparition of the sequence.)\n[…]\nSuppose that K is a finite field and that the rank of apparition r of (W#x5F;n) is at least 4.",
          "type": "quote"
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        {
          "text": "1996, D. L. Wells, Residue Counts Modulo Three for the Fibonacci Triangle, G. E. Bergum, Andreas N. Philippou, Alwyn F. Horadam (editors), Applications of Fibonacci Numbers, Kluwer Academic, Softcover reprint, page 535,\nA similar identification between Pascal's Triangle modulo p and the Fibonacci Triangle modulo p can be made for primes p which have the length of the period equal to twice their rank of apparition in the Fibonacci Sequence."
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          "ref": "2013, E. L. Roettger, H. C. Williams, R. K. Guy, “Some Extensions of the Lucas Functions”, in Jonathan M. Borwein, Igor Shparlinski, Wadim Zudilin, editors, Number Theory and Related Fields, Springer, page 303:",
          "text": "Indeed, as shown in [18, Theorem 4.27], there exist sequences #x5C;#x7B;U#x5F;n#x5C;#x7D; and primes p for which p has three ranks of apparition. In the previous section, we showed that if p#x3D;2, then p has no more than two ranks of apparition in #x5C;#x7B;U#x5F;n#x5C;#x7D;.",
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        "such an index for some generalisation of the concept (for example to allow multiple ranks of apparition for a given m)."
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        "(number theory) Given a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m;"
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          "english": "for the [[Fibonacci sequence]]",
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          "text": "Let (W#x5F;n) be an EDS^([Elliptic Divisibility Sequence]) associated to an elliptic curve E#x2F;K and a nonzero point P#x5C;inE(K) of finite order. Let r#x5C;ge 2 be the smallest index such that W#x5F;r#x3D;0. (The number r is called the rank of apparition of the sequence.)\n[…]\nSuppose that K is a finite field and that the rank of apparition r of (W#x5F;n) is at least 4.",
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          "text": "1996, D. L. Wells, Residue Counts Modulo Three for the Fibonacci Triangle, G. E. Bergum, Andreas N. Philippou, Alwyn F. Horadam (editors), Applications of Fibonacci Numbers, Kluwer Academic, Softcover reprint, page 535,\nA similar identification between Pascal's Triangle modulo p and the Fibonacci Triangle modulo p can be made for primes p which have the length of the period equal to twice their rank of apparition in the Fibonacci Sequence."
        },
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          "ref": "2013, E. L. Roettger, H. C. Williams, R. K. Guy, “Some Extensions of the Lucas Functions”, in Jonathan M. Borwein, Igor Shparlinski, Wadim Zudilin, editors, Number Theory and Related Fields, Springer, page 303:",
          "text": "Indeed, as shown in [18, Theorem 4.27], there exist sequences #x5C;#x7B;U#x5F;n#x5C;#x7D; and primes p for which p has three ranks of apparition. In the previous section, we showed that if p#x3D;2, then p has no more than two ranks of apparition in #x5C;#x7B;U#x5F;n#x5C;#x7D;.",
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        "Given a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m;\nsuch an index for some generalisation of the concept (for example to allow multiple ranks of apparition for a given m).",
        "such an index for some generalisation of the concept (for example to allow multiple ranks of apparition for a given m)."
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