Primitive prime factors in second order linear recurrence sequences

Abstract

For a class of Lucas sequences $x_n$, we show that if $n$ is a positive integer then $x_n$ has a primitive prime factor which divides $x_n$ to an odd power, except perhaps when $n=1,2,3or6$. This has several desirable consequences.

To Andrzej Schinzel on his 75th birthday