English

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

Number Theory 2019-02-21 v1

Abstract

We show that there are arbitrarily large sets SS of ss primes for which the number of solutions to a+1=ca+1=c where all prime factors of acac lie in SS has exp(s1/4/logs)\gg \exp( s^{1/4}/\log s) solutions.

Keywords

Cite

@article{arxiv.1902.07397,
  title  = {Many solutions to the $S$-unit equation $a+1=c$},
  author = {Junsoo Ha and Kannan Soundararajan},
  journal= {arXiv preprint arXiv:1902.07397},
  year   = {2019}
}

Comments

7 pages

R2 v1 2026-06-23T07:45:39.790Z