IMO Shortlist 1991 problem 22
Dodao/la:
arhiva2. travnja 2012. Let
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
and
![g](/media/m/9/5/8/958b2ae8c90cadb8c953ce50efb9c02a.png)
be two integer-valued functions defined on the set of all integers such that
(a)
![f(m + f(f(n))) = -f(f(m+ 1) - n](/media/m/a/3/4/a3411f873d33e130c1f4bf42bf8f334f.png)
for all integers
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
and
(b)
![g](/media/m/9/5/8/958b2ae8c90cadb8c953ce50efb9c02a.png)
is a polynomial function with integer coefficients and g(n) =
%V0
Let $f$ and $g$ be two integer-valued functions defined on the set of all integers such that
(a) $f(m + f(f(n))) = -f(f(m+ 1) - n$ for all integers $m$ and $n;$
(b) $g$ is a polynomial function with integer coefficients and g(n) = $g(f(n))$ $\forall n \in \mathbb{Z}.$
Izvor: Međunarodna matematička olimpijada, shortlist 1991