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Bounds on the number of squares in recurrence sequences

Number Theory 2025-09-19 v3

Abstract

We investigate the number of squares in a very broad family of binary recurrence sequences with u0=1u_{0}=1. We show that there are at most two distinct squares in such sequences (the best possible result), except under such very special conditions where we prove there are at most three such squares.

Keywords

Cite

@article{arxiv.2401.01293,
  title  = {Bounds on the number of squares in recurrence sequences},
  author = {Paul M Voutier},
  journal= {arXiv preprint arXiv:2401.01293},
  year   = {2025}
}

Comments

Published version plus corrections (see last section)