English

Primitive prime factors in second order linear recurrence sequences

Number Theory 2013-01-01 v1

Abstract

For a class of Lucas sequences xn{x_n}, we show that if nn is a positive integer then xnx_n has a primitive prime factor which divides xnx_n to an odd power, except perhaps when n=1,2,3or6n = 1, 2, 3 or 6. This has several desirable consequences.

Keywords

Cite

@article{arxiv.1212.6306,
  title  = {Primitive prime factors in second order linear recurrence sequences},
  author = {Andrew Granville},
  journal= {arXiv preprint arXiv:1212.6306},
  year   = {2013}
}

Comments

To Andrzej Schinzel on his 75th birthday

R2 v1 2026-06-21T23:00:39.135Z