Affiliation:
1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, India
Abstract
We consider the two Diophantine equations ym = F(x) and G(y) = F(x) under the assumption that gcd (m, deg F) > 1 and gcd ( deg G, deg F) > 1, respectively. We prove that the bounds for the denominator of the coefficients of the power series arising from the above two situations can be improved considerably and thus we establish improved upper bounds for the size of the solutions (namely for |x| and |y|). We also give explicit upper bounds for the integer solutions of equations of the form [Formula: see text] under the assumption that [Formula: see text]
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
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