IR-TST 2023 Problem 5

Suppose that $n\ge2$ and $a_1,a_2,...,a_n$ are natural numbers that $(a_1,a_2,...,a_n)=1$ . Find all strictly increasing function $f: \mathbb{Z} \to \mathbb{R}$ that: $$\forall x_1,x_2,...,x_n \in \mathbb{Z} : f(\sum_{i=1}^{n} {x_ia_i}) = \sum_{i=1}^{n} {f(x_ia_i})$$ Proposed by Navid Safaei and Ali Mirzaei