MathDB

Let

n\geq 1

be a positive integer. We say that an integer

k

is a fan of

n

0\leq k\leq n-1

and there exist integers

x,y,z\in\mathbb{Z}

such that \begin{align*} x^2+y^2+z^2 &\equiv 0 \pmod n;\\ xyz &\equiv k \pmod n. \end{align*} Let

f(n)

be the number of fans of

n

. Determine

f(2020)

18