Many solutions to the $S$-unit equation $a+1=c$

Junsoo Ha; Kannan Soundararajan

arxiv: 1902.07397 · v1 · pith:RYLQP5CQnew · submitted 2019-02-20 · 🧮 math.NT

Many solutions to the S-unit equation a+1=c

Junsoo Ha , Kannan Soundararajan This is my paper

classification 🧮 math.NT

keywords solutionsarbitrarilyequationfactorslargemanynumberprime

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We show that there are arbitrarily large sets $S$ of $s$ primes for which the number of solutions to $a+1=c$ where all prime factors of $ac$ lie in $S$ has $\gg \exp( s^{1/4}/\log s)$ solutions.

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Many solutions to the S-unit equation a+1=c

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