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Polynomials that (m,n)=1 implies (p(m),p(n))=1

Source: Iranian National Olympiad (3rd Round) 2004

January 9, 2009
algebrapolynomialnumber theory proposednumber theory

Problem Statement

Find all polynomials p∈Z[x] p\in\mathbb Z[x] such that (m,n)\equal{}1\Rightarrow (p(m),p(n))\equal{}1