Find all polynomials P(x) of the smallest possible degree
Source: Austrian Mathematical Olympiad 2002, Part 2, D2, P1
June 25, 2011
algebrapolynomialalgebra proposed
Problem Statement
Find all polynomials of the smallest possible degree with the following properties:(i) The leading coefficient is ;
(ii) The coefficient at the smallest non-vanishing power is ;
(iii) The sum of all the coefficients is ;
(iv) .