Dictionary

rank of apparition en · NOUN

Meanings

1. Given a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m;
   • Let (W#95;n) be an EDS^([Elliptic Divisibility Sequence]) associated to an elliptic curve E#47;K and a nonzero point P#92;inE(K) of finite order. Let r#92;ge 2 be the smallest index such that W#95;r#61;0. (The number r is called the rank of apparition of the sequence.) […] Suppose that K is a finite field and that the rank of apparition r of (W#95;n) is at least 4. 1986, Joseph H. Silverman, The Arithmetic of Elliptic Curves, Springer, page 114:
   • Indeed, as shown in [18, Theorem 4.27], there exist sequences #92;#123;U#95;n#92;#125; and primes p for which p has three ranks of apparition. In the previous section, we showed that if p#61;2, then p has no more than two ranks of apparition in #92;#123;U#95;n#92;#125;. 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:
   • 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, A 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.
2. Given a positive integer m and a divisibility sequence Sₖ, the smallest index k such that Sₖ is divisible by m; such 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).

Forms

Synonyms

Fibonacci entry point · Fibonacci entry point