ON THE NUMBER OF DIVISORS OF $n^{2}-1$

@article{Dudek2015ONTN,
  title={ON THE NUMBER OF DIVISORS OF \$n^\{2\}-1\$},
  author={Adrian W. Dudek},
  journal={Bulletin of the Australian Mathematical Society},
  year={2015},
  volume={93},
  pages={194 - 198}
}
  • Adrian W. Dudek
  • Published 30 July 2015
  • Mathematics
  • Bulletin of the Australian Mathematical Society
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 $x^{2}\equiv 1~(\text{mod}~d)$. 
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