A generalized Fibonacci-type sequence is defined from a fourth order homogeneous linear recurrence relation, and various divisibility properties are developed. In particular, the notion of a proper… Expand

Brillhart, Montgomery and Silverman [2] have developed tables of Fibonacci and Lucas factorizations. In doing so they have used primitive parts of these numbers. These are analogous to the proper… Expand

Nash [4] used recursive sequences like the Fibonacci numbers, {Fn}, to investigate factors and divisibility. The Fibonacci numbers are defined by
$$ \begin{array}{*{20}{c}} {{F_n} = {F_{n - 1}} +… Expand