Papers › Bounds on the number of squares in recurrence sequences: arbitrary b, III
Bounds on the number of squares in recurrence sequences: arbitrary b, III
Paul M Voutier
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We generalise our earlier work on the number of squares in binary recurrence sequences, { yₖ }_(k ≥-∞). In the notation of our previous papers, here we consider the case when N_α is any negative integer and y₀=b² for any positive integer, b. We show that there are at most 4 distinct squares with yₖ sufficiently large. This allows us to also show that there are at most 9 distinct squares in such sequences when b=1,2 or 3, or once d is sufficiently large.
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