Submission date: 1st April 2024

Abstract:

Generalizing an argument of Matiyasevich, we illustrate a method to generate infinitely many diophantine equations whose solutions can be completely described by linear recurrences. In particular, we provide an integer-coefficient polynomial p(x,y,z) whose only integer roots are consecutive triples of Tribonacci numbers.

Mathematics Subject Classification: 11D72

Keywords and phrases:

Full text arXiv 2404.01483: pdf, ps.