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Indian RMO- Paper -3

Source: RMO - problem 4

December 11, 2013
algebrapolynomialquadraticsmodular arithmeticnumber theory unsolvednumber theory

Problem Statement

A polynomial is called Fermat polynomial if it can be written as the sum of squares of two polynomials with integer coefficients. Suppose that f(x)f(x) is a Fermat polynomial such that f(0)=1000f(0)=1000. Prove that f(x)+2xf(x)+2x is not a fermat polynomial
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