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

@article{Dudek2015ONTN,
  title={ON THE NUMBER OF DIVISORS OF \$n^\{2\}-1\$},
  author={A. Dudek},
  journal={Bulletin of the Australian Mathematical Society},
  year={2015},
  volume={93},
  pages={194 - 198}
}
  • A. Dudek
  • Published 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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References

SHOWING 1-10 OF 17 REFERENCES
Bounds on the number of Diophantine quintuples
  • 20
  • Highly Influential
  • PDF
Multiplicative Number Theory
  • 1,935
There are only finitely many Diophantine quintuples
  • 160
  • PDF
The Theory of the Riemann Zeta-Function
  • 2,718
Van der Corput's method of exponential sums
  • 317
On the number of divisors of quadratic polynomials
  • 88
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