A Mean Value Theorem for the Diophantine Equation $axy-x-y=n$

Details A Mean Value Theorem for the Diophantine Equation $axy-x-y=n$ A Mean Value Theorem for the Diophantine Equation $axy-x-y=n$

2011-07-30

arxiv.org/abs/1108.0095v2

Mathematics

Number Theory

11 pages, to appear in Acta Math. Hungar. A couple of typos are corrected in the new version

Scientific paper

In this paper, we prove an asymptotic formula for the average number of
solutions to the Diophantine equation $axy-x-y=n$ in which $a$ is fixed and and
$n$ varies.

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