Question 7
(FIN), IMO 6. Assume that $f(x,y)$ is defined for all positive integers $x$ and $y$, and that the following equations are satisfied:
$$f(0,y)=y+1,\qquad f(x+1,0)=f(x,1),\qquad f(x+1,y+1)=f(x,f(x+1,y)).$$
Determine $f(2,2)$, $f(3,3)$ and $f(4,4)$.
Alternative version: Determine $f(4,1981)$.
$$f(0,y)=y+1,\qquad f(x+1,0)=f(x,1),\qquad f(x+1,y+1)=f(x,f(x+1,y)).$$
Determine $f(2,2)$, $f(3,3)$ and $f(4,4)$.
Alternative version: Determine $f(4,1981)$.