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Source: Iranian third round 2015 algebra problem 5

September 8, 2015
algebrapolynomialfunctionIranfunctional equation

Problem Statement

Find all polynomials p(x)∈R[x]p(x)\in\mathbb{R}[x] such that for all x∈Rx\in \mathbb{R}: p(5x)2−3=p(5x2+1)p(5x)^2-3=p(5x^2+1) such that: a)p(0)≠0a) p(0)\neq 0 b)p(0)=0b) p(0)=0
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