IMO Shortlist 1977 problem 9
Dodao/la:
arhiva2. travnja 2012. For which positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
do there exist two polynomials
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
and
![g](/media/m/9/5/8/958b2ae8c90cadb8c953ce50efb9c02a.png)
with integer coefficients of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
variables
![x_1, x_2, \ldots , x_n](/media/m/7/6/6/76648c55550ff7d9bec21ad793340730.png)
such that the following equality is satisfied:
%V0
For which positive integers $n$ do there exist two polynomials $f$ and $g$ with integer coefficients of $n$ variables $x_1, x_2, \ldots , x_n$ such that the following equality is satisfied:
$$\sum_{i=1}^n x_i f(x_1, x_2, \ldots , x_n) = g(x_1^2, x_2^2, \ldots , x_n^2) \ ?$$
Izvor: Međunarodna matematička olimpijada, shortlist 1977