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