On the Number of Divisors of $n^2-1$

Abstract

We prove an asymptotic formula for the sum ${\sum }_{n\le N}d(n^2-1)$, 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 ${\sum }_{d\le N}g(d)$, where $g(d)$ denotes the number of solutions $x$ in ${\mathbb{Z}}_d$ to the equation $x^2\equiv 1\mathrm{mod}d$.

7 pages

Cited by in corpus (1)

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