MathDB
Coefficient of a cubic equations

Source: Baltic Way 2009

December 4, 2009
number theory proposednumber theory

Problem Statement

Let a a and b b be integers such that the equation x^3\minus{}ax^2\minus{}b\equal{}0 has three integer roots. Prove that b\equal{}dk^2, where d d and k k are integers and d d divides a a.