Abstract
For an integer \(d\ge 2\) which is not a square, we show that there is at most one value of the positive integer x participating in the Pell equation \(x^2-dy^2=\pm \,4\) which is a Tribonacci number, with a few exceptions that we completely characterize.
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Acknowledgements
The authors are grateful to the anonymous referee for the careful reading the manuscript. F. L. was supported in parts by Grants CPRR160325161141 of NRF (South Africa) CGA 17-02804S (Czech Republic). B. K and A. T. are partially supported by Purdue University Northwest, IN.
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Kafle, B., Luca, F. & Togbé, A. x-Coordinates of Pell equations which are Tribonacci numbers II. Period Math Hung 79, 157–167 (2019). https://doi.org/10.1007/s10998-018-0264-x
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DOI: https://doi.org/10.1007/s10998-018-0264-x