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RMO 2013 C4

  • CRMO Paper 3

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

Dataset text AI-MO AoPS. Quoted with source.

Official text: Indian Regional Mathematical Olympiad 2013 official paper, page 1.

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