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