Geodesic
A note on the diophantine equation ${k\choose 2}-1=q^n+1$
Colloquium Mathematicum, Tome 76 (1998) no. 1, pp. 31-34.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $n\lt 2\cdot 10^{17}$.
DOI : 10.4064/cm-76-1-31-34

Maohua Le 1

1 
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Maohua Le. A note on the diophantine equation ${k\choose 2}-1=q^n+1$. Colloquium Mathematicum, Tome 76 (1998) no. 1, pp. 31-34. doi : 10.4064/cm-76-1-31-34. http://geodesic.mathdoc.fr/articles/10.4064/cm-76-1-31-34/

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