I want to know how to compute this function:
$f : \mathbb{Z}_m \rightarrow \mathbb{N}$
$f(z) = |\{ (x, y) \in \mathbb{Z}_m^2 \mid \langle x, y\rangle = z \}|$
where $\langle x, y\rangle = \sum_{i \in [m]}x_iy_i$.
How many pairs of numbers between 0 and n-1 are equal to z mod n?
Samuel Schlesinger
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