The distribution of second order linear recurrence sequences mod $2^m$

On Second-order Linear Recurrence Sequences: Wall and Wyler Revisited

Sequences of integers satisfying linear recurrence relations have been studied extensively since the time of Lucas [5], notable contributions being made by Carmichael [2], Lehmer [4], Ward [11], and more recently by many others. In this paper we obtain a unified theory of the structure of recurrence sequences by examining the ratios of recurrence sequences that satisfy the same recurrence relat...

Primitive Prime Factors in Second-order Linear Recurrence Sequences

For a class of Lucas sequences {xn}, we show that if n is a positive integer then xn has a primitive prime factor which divides xn to an odd power, except perhaps when n = 1, 2, 3 or 6. This has several desirable consequences.

Uniform Distribution of Second-order Linear Recurring Sequences

A complete classification is obtained for all second-order linear recurring sequences uniformly distributed modulo an ideal of a Dedekind domain.

Pseudoprimes for Higher-order Linear Recurrence Sequences

With the advent of high-speed computing, there is a rekindled interest in the problem of determining when a given whole number N > 1 is prime or composite. While complex algorithms have been developed to settle this for 200-digit numbers in a matter of minutes with a supercomputer, there is a need for simpler, more practical algorithms for dealing with numbers of a more modest size. Such practi...

Intersections of Second - Order Linear Recursive Sequences