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A note on the diophantine equation ${k\choose 2}-1=q^n+1$

Volume 76 / 1998

Maohua Le 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 $n\lt 2\cdot 10^{17}$.

Authors

  • Maohua Le

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