Bounds on the number of squares in recurrence sequences

Abstract

We investigate the number of squares in a very broad family of binary recurrence sequences with $u_0=1$. 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.

Published version plus corrections (see last section)

References in corpus (1)

• Improved Constants for Effective Irrationality Measures from Hypergeometric Functions

Cited by in corpus (1)

• Bounds on the number of squares in recurrence sequences: $y_0=b^2$ (I)