A note on the diophantine equation ${k\choose 2}-1=q^n+1$
Volume 76 / 1998
Colloquium Mathematicum 76 (1998), 31-34
DOI: 10.4064/cm-76-1-31-34
Abstract
In this note we prove that the equation ${k\choose 2}-1=q^n+1$, $q\ge 2, n\ge 3$, has only finitely many positive integer solutions $(k,q,n)$. Moreover, all solutions $(k,q,n)$ satisfy $k\lt10^{10^{182}}$, $q\lt10^{10^{165}}$ and $n\lt 2\cdot 10^{17}$.
