arXiv subjects

Ashleigh Wilcox

Publications and source records attributed to Ashleigh Wilcox.

2 recordsLinked to original sources

arXiv2024

A systematic approach to Diophantine equations: two thousand solved examples

Monograph "B. Grechuk, Polynomial Diophantine equations. A systematic approach" suggests solving Diophantine equations systematically in certain order. Many hundreds of the equations are left to the reader. Here, we provide complete solutions to all these equations. The difficulties of solved equations range from elementary to research level. In the last section, we present a summary table of all solved equations ordered by their size, which makes them easy to find. As a result, this document may be used as a database of solved Diophantine equations of small size, to which more difficult equations can be reduced.

math.GM↗

arXiv2023

Diophantine equations with three monomials

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 $x^4+axy+y^3=0$ 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 $100\%$ of three-monomial equations as the number of variables goes to infinity.

math.NT↗