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

Abstract

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.

arXiv comment7 pages

References in corpus (2)

• Bombieri--Vinogradov and Barban--Davenport--Halberstam type theorems for smooth numbers
• Counting Smooth Solutions to the Equation A+B=C

Cited by in corpus (1)

• Counting solvable $S$-unit equations