21. (CZS 2) Let $a_{0}, a_{1}, \ldots, a_{k}(k \geq 1)$ be positive integers. Find all positive integers $y$ such that
$$
a_{0}\left|y ;\left(a_{0}+a_{1}\right)\right|\left(y+a_{1}\right) ; \ldots ;\left(a_{0}+a_{n}\right) \mid\left(y+a_{n}\right) .
$$
21. The given conditions are equivalent to $y-a_{0}$ being divisible by $a_{0}, a_{0}+$ $a_{1}, a_{0}+a_{2}, \ldots, a_{0}+a_{n}$, i.e., to $y=k\left[a_{0}, a_{0}+a_{1}, \ldots, a_{0}+a_{n}\right]+a_{0}, k \in \mathbb{N}_{0}$.