divisibility sequences

Noun

divisibility sequence (plural divisibility sequences)

1. Any sequence of integers {aₙ}, indexed by the natural numbers, such that if n is divisible by m then aₙ is divisible by aₘ.
   • 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...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...