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Wiktionary英語版での「divisibility sequence」の意味 |
divisibility sequence
名詞
divisibility sequence (複数形 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, 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 .
- 2012, P. Ingram, J. H. Silverman, Primitive Divisors in Elliptic Divisibility Sequences, Dorian Goldfeld, Jay Jorgenson, Peter Jones, Dinakar Ramakrishnan, Kenneth Ribet, John Tate (editors), Number Theory, Analysis and Geometry, Springer, page 244,
使用する際の注意点
The concept can be generalised to sequences of elements of any ring for which divisibility is defined.
派生語
- strong divisibility sequence
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divisibility sequences
Wiktionary英語版
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divisibility
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rank of apparition
Wiktionary英語版
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意味 |
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