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$n^{2}-1$
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 
$x^{2}\equiv 1~(\text{mod}~d)$.
