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Bosnia and Herzegovina JBMO TST 2010 Problem 2

Source: Bosnia and Herzegovina Junior Balkan Mathematical Olympiad TST 2010

September 17, 2018

polynomialalgebraminimization

Problem Statement

Let us consider every third degree polynomial

P(x)

with coefficients as nonnegative positive integers such that

P(1)=20

. Among them determine polynomial for which is:

a)

Minimal value of

P(4)

b)

Maximal value of

P(3)/P(2)