On the X-coordinates of Pell equations which are Tribonacci numbers

2016/12/30 by Florian Luca, Luca, Florian, Amanda Montejano +5
Physics and Astronomy · Mathematics · #Advanced Mathematical Theories and Applications #Advanced Combinatorial Mathematics #Advanced Mathematical Identities

paper · pdf · doi:10.48550/arxiv.1612.09546

Abstract

For an integer d≥ 2 which is not a square, we show that there is at most one value of the positive integer X participating in the Pell equation X²-dY²=± 1 which is a Tribonacci number, with a few exceptions that we completely characterize.

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