The sum of two S-units being a perfect power in global function fields
István Gaál, Michael E. Pohst · Mathematica Slovaca · 2013
Abstract Let x 1 and x 2 be integers divisible only by some fixed primes. Is it possible that x 1+x 2 is a perfect power? Special cases of the equation x 1+x 2 = y k were formerly considered over ℤ. In this paper we develop an algorithm to solve this equation over global algebraic function fields. Our method is illustrated by two explicit examples.