IMO Shortlist 1981 problem 7
Dodao/la:
arhiva2. travnja 2012. The function
![f(x,y)](/media/m/a/9/e/a9e336e9bf3c0902c74277ab2009fb5e.png)
satisfies:
![f(0,y)=y+1, f(x+1,0) = f(x,1), f(x+1,y+1)=f(x,f(x+1,y))](/media/m/8/6/7/867f31ff7b5eb54902aeea31215e5acc.png)
for all non-negative integers
![x,y](/media/m/f/b/6/fb60533620f22cd699e5b58ce9a646a4.png)
. Find
![f(4,1981)](/media/m/3/4/7/3471e03f5adc2a3c89639a9a0b7a0008.png)
.
%V0
The function $f(x,y)$ satisfies: $f(0,y)=y+1, f(x+1,0) = f(x,1), f(x+1,y+1)=f(x,f(x+1,y))$ for all non-negative integers $x,y$. Find $f(4,1981)$.
Izvor: Međunarodna matematička olimpijada, shortlist 1981