MathDB

Determine a monic cubic

Source: Finland 2013, Problem 1

May 2, 2013

algebrapolynomialquadraticsalgebra unsolved

Problem Statement

The coefficients

a,b,c

of a polynomial

f:\mathbb{R}\to\mathbb{R}, f(x)=x^3+ax^2+bx+c

are mutually distinct integers and different from zero. Furthermore,

f(a)=a^3

and

f(b)=b^3.

Determine

a,b

and

c