MathDB

12

Part of 1976 IMO Shortlist

Problems(1)

Decomposing a polynomial into a sum of polynomials

Source:

9/20/2010
The polynomial 1976(x+x2+⋯+xn)1976(x+x^2+ \cdots +x^n) is decomposed into a sum of polynomials of the form a1x+a2x2+⋯+anxna_1x + a_2x^2 + \cdots + a_nx^n, where a1,a2,…,ana_1, a_2, \ldots , a_n are distinct positive integers not greater than nn. Find all values of nn for which such a decomposition is possible.
algebrapolynomialAdditive combinatoricscountingcombinatoricsIMO Shortlist