Constant Function

Algebra Level pending

Consider the sets \[\begin{align} \ X &= \{ -5, 0, 5 \}\\ Y & = \{ y \mid -3 \leq y \leq 3,\ y \in \mathbf{Z} \}. \end{align}\] How many functions \( f: X \rightarrow Y \) are there such that \( x \cdot f(x) \) is a constant for all elements \(x\) in \(X\)?

Details and assumptions

\( \mathbf{Z} \) is the set of integers.

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