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ON THE NUMBER OF DIVISORS OF
$n^{2}-1$
Published online by Cambridge University Press: 02 October 2015
Abstract
We prove an asymptotic formula for the sum $\sum _{n\leq N}d(n^{2}-1)$, where
$d(n)$ denotes the number of divisors of
$n$. During the course of our proof, we also furnish an asymptotic formula for the sum
$\sum _{d\leq N}g(d)$, where
$g(d)$ denotes the number of solutions
$x$ in
$\mathbb{Z}_{d}$ to the equation
$x^{2}\equiv 1~(\text{mod}~d)$.
MSC classification
- Type
- Research Article
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- Copyright
- © 2015 Australian Mathematical Publishing Association Inc.
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