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arXiv · 1610.04295

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

Jose Maria Grau·A. Oller-marcen
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Abstract

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

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Jose Maria Grau, A. Oller-marcen. 2016-10-13. Fast computation of the number of solutions to $x_1^2+\cdots+x_k^2 \equiv \lambda \pmod{n}$. https://arxiv.org/abs/1610.04295

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