Diophantine equations with three monomials
Number Theory
2023-07-07 v1
Abstract
We present a general algorithm for solving all two-variable polynomial Diophantine equations consisting of three monomials. Before this work, even the existence of an algorithm for solving the one-parameter family of equations has been an open question. We also present an elementary method that reduces the task of finding all integer solutions to a general three-monomial equation to the task of finding primitive solutions to equations with three monomials in disjoint variables. We identify a large class of three-monomial equations for which this method leads to a complete solution. Empirical data suggests that this class contains of three-monomial equations as the number of variables goes to infinity.
Cite
@article{arxiv.2307.02513,
title = {Diophantine equations with three monomials},
author = {Bogdan Grechuk and Tetiana Grechuk and Ashleigh Wilcox},
journal= {arXiv preprint arXiv:2307.02513},
year = {2023}
}