divisibility sequence
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English
[edit]Noun
[edit]divisibility sequence (plural divisibility sequences)
- (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.
- 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:
- If is any divisibility sequence, one says that a prime is a primitive divisor of if but . Primitive divisors of certain divisibility sequences were studied by Zsigmondy [37] in the 19th century.
- 2013, Graham Everest, Thomas Ward, Heights of Polynomials and Entropy in Algebraic Dynamics, Springer, page 138:
- These divisibility sequences satisfy the same recurrence relations as the polynomials and (see Appendix C).
- 2021, Masum Billal, Samin Riasat, Integer Sequences, Springer, page 59:
- Moreover, in order to keep a divisibility sequence normalized, we can assume without loss of generality that = 0 and .
Usage notes
[edit]The concept can be generalised to sequences of elements of any ring for which divisibility is defined.
Derived terms
[edit]Translations
[edit]type of integer sequence
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Further reading
[edit]Elliptic divisibility sequence on Wikipedia.Wikipedia
Fibonacci number § Divisibility properties on Wikipedia.Wikipedia