Question 82
A function $f$ is defined on the set of positive integers $N$ and takes positive integers as its values. It is known that for all $n \ge 3$
$$
f(n) = \lceil \sqrt{f(n-1)f(n-2)} + n \rceil
$$
Prove that there is an integer $n$ such that $f(n) = n$.
$$
f(n) = \lceil \sqrt{f(n-1)f(n-2)} + n \rceil
$$
Prove that there is an integer $n$ such that $f(n) = n$.