Word.ws English Dictionary

divisibility sequence

divisibility sequence noun: any sequence of integers {aₙ}, indexed by the natural numbers, such that if n is divisible by m then aₙ is divisible by aₘ.

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...
    • These divisibility sequences satisfy the same recurrence relations as the polynomials #92;phi#95;n and #92;psi²#95;n (see Appendix C).2013, Graham Everest, Thomas Ward, Heights of Polynomials and Entropy in Algebraic Dynamics, Springer, page 138

Examples of divisibility sequence in a sentence

  • Primitive divisors of certain divisibility sequences were studied by Zsigmondy [37] in the 19ᵗʰ century.2012, P. Ingram, J. H. Silverman, “Primitive Divisors in Elliptic Divisibility Sequences”, in Dorian Goldfeld, Jay Jorgenson, Peter Jones...
  • Moreover, in order to keep a divisibility sequence normalized, we can assume without loss of generality that a#95;0 = 0 and a#95;1#61;1.2021, Masum Billal, Samin Riasat, Integer Sequences, Springer, page 59:

Forms of divisibility sequence

pluraldivisibility sequences

Words formed from divisibility sequence

  • strong divisibility sequence

Questions about divisibility sequence

What does divisibility sequence mean?
Divisibility sequence means any sequence of integers {aₙ}, indexed by the natural numbers, such that if n is divisible by m then aₙ is divisible by aₘ.
How do you use divisibility sequence in a sentence?
Primitive divisors of certain divisibility sequences were studied by Zsigmondy [37] in the 19ᵗʰ century.
What part of speech is divisibility sequence?
Divisibility sequence is a noun.
What is the plural of divisibility sequence?
The plural of divisibility sequence is divisibility sequences.

Words near divisibility sequence in the dictionary

  1. divisibilism
  2. divisibilist
  3. divisibilists
  4. divisibilities
  5. divisibility
  6. divisibility sequence
  7. divisibility sequences
  8. divisible
  9. divisibleness
  10. divisibles
  11. divisibly

Source and license

Adapted from Wiktionary: divisibility sequence (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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