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Part of 2021 Mediterranean Mathematics Olympiad

Problems(1)

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

Source: 2021 Mediterranean Mathematical Olympiad P1 MMC

9/11/2021
Determine the smallest positive integer MM with the following property: For every choice of integers a,b,ca,b,c, there exists a polynomial P(x)P(x) with integer coefficients so that P(1)=aMP(1)=aM and P(2)=bMP(2)=bM and P(4)=cMP(4)=cM.
Proposed by Gerhard Woeginger, Austria
algebrapolynomialInteger Polynomial