# Thue-Mahler equation

Let $F \in \mathbb{Z}[X,Y]$ be an homogenous polynomial. An equation of the form $$ F(X,Y) = d p_1^{a_1}\cdots p_n^{a_n},$$ with $p_1, \cdots, p_n$ are prime numbers and $d \in \mathbb{Z}$ is called a Thue-Mahler equation. Is there an explicit function in sage that can solve this kind of equations even if is a simpler case such as F(x,y) = p^a ?. I have been looking for this with no result.

It seems not. There is Magma code in the master's thesis Implementation of a Thue-Mahler equation solver by Kyle Hambrook.