One-Parameter Families of Unit Equations

Details One-Parameter Families of Unit Equations One-Parameter Families of Unit Equations

2006-01-27

arxiv.org/abs/math/0601685v1

Mathematics

Number Theory

10 pages

Scientific paper

We study one-parameter families of S-unit equations of the form f(t)u+g(t)v=h(t), where f, g, and h are univariate polynomials over a number field, t is an S-integer, and u and v are S-units. For many possible choices of f, g, and h, we are able to determine all but finitely many solutions to the corresponding one-parameter family of S-unit equations. The results are obtained as consequences of some recent results on integral points on surfaces.

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