The Thue-Mahler equation is a type of Diophantine equation that generalizes the classical Thue equation by allowing the coefficients to be subject to specific conditions related to a given set of rational numbers. It aims to find integer solutions to equations of the form $f(x, y) = z$, where $f$ is a polynomial and $z$ is a product of prime powers constrained by certain norms. This equation connects deeply with number theory and has significant implications in arithmetic geometry.
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