IMO Shortlist 1976 problem 12
Dodao/la:
arhiva2. travnja 2012. The polynomial
![1976(x+x^2+ \cdots +x^n)](/media/m/7/3/5/7358d600e639b90bda548f7655032c6f.png)
is decomposed into a sum of polynomials of the form
![a_1x + a_2x^2 + \cdots + a_nx^n](/media/m/c/6/8/c68d24fb1e91c896f972c2ca2cb7dcdd.png)
, where
![a_1, a_2, \ldots , a_n](/media/m/0/a/8/0a84730daafb8c167c30263462061224.png)
are distinct positive integers not greater than
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
. Find all values of
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
for which such a decomposition is possible.
%V0
The polynomial $1976(x+x^2+ \cdots +x^n)$ is decomposed into a sum of polynomials of the form $a_1x + a_2x^2 + \cdots + a_nx^n$, where $a_1, a_2, \ldots , a_n$ are distinct positive integers not greater than $n$. Find all values of $n$ for which such a decomposition is possible.
Izvor: Međunarodna matematička olimpijada, shortlist 1976