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Two $S$-unit equations with many solutions by Konyagin, S.; Soundararajan, K. is a scholarly article available to read on EtoBox.

What is Two $S$-unit equations with many solutions about?

We show that there exist arbitrarily large sets $S$ of $s$ prime numbers such that the equation $a+b=c$ has more than $\exp(s^{2-\sqrt{2}-\epsilon})$ 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 $\exp(s^{\frac 1{16}})$ solutions with all prime factors of $a$ and $c$ lying in $S$.

Author

Konyagin, S.; Soundararajan, K.

Published

2006

Language

EN