Problem 7

Let the function $f:\mathbb{N}^{2}\to\mathbb{N}$ be defined such that

Prove that

1. $f(n,2)=n-1$ for all integers $n>1$;

2. $f(n+1,n)=2$ for all positive integers $n$; and

3. $f(n,4)=2$ for all integers $n>1$.