Problem

Source: 2017 Saudi Arabia BMO TST II p2

Tags: algebra, Integer Polynomial, polynomial



Polynomial P(x) with integer coefficient is called cube-presented if it can be represented as sum of several cube of polynomials with integer coefficients. Examples: 3x+3x2 is cube-represented because 3x+3x2=(x+1)3+(x)3+(1)3. a) Is 3x2 a cube-represented polynomial? b). How many quadratic polynomial P(x) with integer coefficients belong to the set {1,2,3,...,2017} which is cube-represented?