Abstract
Let $k \ge 2$ be an integer and let ${\mc A}$ and ${\mc B}$ be two sets of integers. We give upper bounds for the number of perfect $k$-th powers of the form $ab+1$, with $a$ in ${\mc A}$ and $b$ in ${\mc B}$. We further investigate several related questions.
Citation
Yann Bugeaud. Katalin Gyarmati. "On generalizations of a problem of Diophantus." Illinois J. Math. 48 (4) 1105 - 1115, Winter 2004. https://doi.org/10.1215/ijm/1258138502
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