VN-TST 1995 Problem 5

For any nonnegative integer $n$ , let $f(n)$ be the greatest integer such that $2^{f(n)} | n + 1$ . A pair $(n, p)$ of nonnegative integers is called nice if $2^{f(n)} > p$ . Find all triples $(n, p, q)$ of nonnegative integers such that the pairs $(n, p)$ , $(p, q)$ and $(n + p + q, n)$ are all nice.