MathDB
Interesting Polynomial

Source: 2017 Taiwan TST Round 3

April 13, 2018
algebrapolynomial

Problem Statement

Prove that there exists a polynomial with integer coefficients satisfying the following conditions: (a)f(x)=0f(x)=0 has no rational root. (b) For any positive integer nn, there always exists an integer mm such that n∣f(m)n\mid f(m).
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