Two S-unit equations with many solutions |
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| Authors: | S Konyagin |
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| Institution: | a Department of Mathematics and Mechanics, Moscow State University, Moscow 119992, Russia
b Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA |
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| Abstract: | We show that there exist arbitrarily large sets S of s prime numbers such that the equation a+b=c has more than  solutions in coprime integers a, b, c all of whose prime factors lie in the set S. We also show that there exist sets S for which the equation a+1=c has more than  solutions with all prime factors of a and c lying in S. |
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