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Romanian National Olympiad 2018 - Grade 12 - problem 4

Source: Romania NMO - 2018

April 7, 2018
polynomialIrreduciblesuperior algebra

Problem Statement

For any k∈Z,k \in \mathbb{Z}, define Fk=X4+2(1−k)X2+(1+k)2.F_k=X^4+2(1-k)X^2+(1+k)^2. Find all values k∈Zk \in \mathbb{Z} such that FkF_k is irreducible over Z\mathbb{Z} and reducible over Zp,\mathbb{Z}_p, for any prime p.p.
Marius Vladoiu
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