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P(n) is a three-digit integer for n=1,2,..,1998

Source: Baltic Way 1998

January 11, 2011
algebrapolynomialmodular arithmeticnumber theory proposednumber theory

Problem Statement

Let PP be a polynomial with integer coefficients. Suppose that for n=1,2,3,…,1998n=1,2,3,\ldots ,1998 the number P(n)P(n) is a three-digit positive integer. Prove that the polynomial PP has no integer roots.
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