Two $S$-unit equations with many solutions

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dc.creatorKonyagin, S.
dc.creatorSoundararajan, K.
dc.date2006-04-20
dc.date.accessioned2026-07-07T07:11:09Z
dc.date.available2026-07-07T07:11:09Z
dc.descriptionWe show that there exist arbitrarily large sets $S$ of $s$ prime numbers such that the equation $a+b=c$ has more than $\exp(s^{2-\sqrt{2}-ε})$ 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 $S$.
dc.description6 pages
dc.identifierhttps://arxiv.org/abs/math/0604453
dc.identifierhttp://arxiv.org/abs/math/0604453
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/111644
dc.subjectNumber Theory
dc.titleTwo $S$-unit equations with many solutions
dc.typetext

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