MathDB

Polynomial and binomial coefficient

Source: IMO LongList 1988, Vietnam 5, Problem 93 of ILL

November 9, 2005

algebrapolynomialalgebra unsolved

Problem Statement

Given a natural number

n,

find all polynomials

P(x)

of degree less than

n

satisfying the following condition

\sum^n_{i=0} P(i) \cdot (-1)^i \cdot \binom{n}{i} = 0.