All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 11 Next

Displaying 201 – 220 of 497

Showing per page

Linear recurrence sequences without zeros

Artūras Dubickas, Aivaras Novikas (2014)

Czechoslovak Mathematical Journal

Let a d - 1 , ⋯ , a 0 ∈ ℤ , where d ∈ ℕ and a 0 ≠ 0 , and let X = ( x n ) n = 1 ∞ be a sequence of integers given by the linear recurrence x n + d = a d - 1 x n + d - 1 + ⋯ + a 0 x n for n = 1 , 2 , 3 , ⋯ . We show that there are a prime number p and d integers x 1 , ⋯ , x d such that no element of the sequence X = ( x n ) n = 1 ∞ defined by the above linear recurrence is divisible by p . Furthermore, for any nonnegative integer s there is a prime number p ≥ 3 and d integers x 1 , ⋯ , x d such that every element of the sequence X = ( x n ) n = 1 ∞ defined as above modulo p belongs to the set { s + 1 , s + 2 , ⋯ , p - s - 1 } .

Currently displaying 201 – 220 of 497