Problem

Source: 2021 Mediterranean Mathematical Olympiad P1 MMC

Tags: algebra, polynomial, Integer Polynomial



Determine the smallest positive integer M with the following property: For every choice of integers a,b,c, there exists a polynomial P(x) with integer coefficients so that P(1)=aM and P(2)=bM and P(4)=cM. Proposed by Gerhard Woeginger, Austria