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Q(x)=(x^2+6x+10) * P^2(x) - 1

Source: Vietnam TST 2002 for the 43th IMO, problem 5

June 26, 2005
algebrapolynomialcalculusderivativeparameterizationDiophantine equationalgebra unsolved

Problem Statement

Find all polynomials P(x)P(x) with integer coefficients such that the polynomial Q(x)=(x2+6x+10)⋅P2(x)−1 Q(x)=(x^2+6x+10) \cdot P^2(x)-1 is the square of a polynomial with integer coefficients.
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