A note on the diophantine equation
Tom 76 / 1998
Colloquium Mathematicum 76 (1998), 31-34
DOI: 10.4064/cm-76-1-31-34
Streszczenie
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}.
