MathDB
Existence of polynomial

Source: Korea National 2013 #3

November 10, 2013
algebrapolynomialquadraticsinductioncalculusintegrationmodular arithmetic

Problem Statement

Prove that there exist monic polynomial f(x)f(x) with degree of 6 and having integer coefficients such that (1) For all integer mm, f(m)≠0f(m) \ne 0. (2) For all positive odd integer nn, there exist positive integer kk such that f(k)f(k) is divided by nn.
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