Meaning of divisibility sequence | Babel Free

Definitions

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

Equivalents

Examples

“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 century.”

“These divisibility sequences satisfy the same recurrence relations as the polynomials #92;phi#95;n and #92;psi²#95;n (see Appendix C).”

“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.”

CEFR level