Many solutions to the S-unit equation $$a + 1 = c$$
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DOI: 10.1007/s10474-019-00948-z
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. read more here.
Keywords: solutions unit; unit equation; many solutions;