KURSCHAK 1959

$a, b, c$ are three distinct integers and $n$ is a positive integer. Show that $$\frac{a^n}{(a - b)(a - c)}+\frac{ b^n}{(b - a)(b - c)} +\frac{ c^n}{(c - a)(c - b)}$$ is an integer.

The angles subtended by a tower at distances $100$ , $200$ and $300$ from its foot sum to $90^o$ . What is its height?