English

Fast computation of the number of solutions to $x_1^2+\cdots+x_k^2 \equiv \lambda \pmod{n}$

Number Theory 2016-10-17 v1

Abstract

In this paper we study the multiplicative function ρk,λ(n)\rho_{k,\lambda}(n) that counts the number of incongruent solutions of the equation x12++xk2λ(modn)x_1^2+\cdots+x_k^2 \equiv \lambda\pmod{n}. In particular we give closed explicit formulas for ρk,λ(ps)\rho_{k,\lambda}(p^s) with a arithmetic complexity of constant order.

Keywords

Cite

@article{arxiv.1610.04295,
  title  = {Fast computation of the number of solutions to $x_1^2+\cdots+x_k^2 \equiv \lambda \pmod{n}$},
  author = {Jose Maria Grau and A. Oller-marcen},
  journal= {arXiv preprint arXiv:1610.04295},
  year   = {2016}
}