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min M, exists integer Polynomial P, P(1)=aM , P(2)=bM, P(4)=cM

Source: 2021 Mediterranean Mathematical Olympiad P1 MMC

September 11, 2021

algebrapolynomialInteger Polynomial

Problem Statement

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