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Polynomial

Source: Canadian Mathematical Olympiad 1976 Problem 7

October 23, 2008
algebrapolynomialalgebra proposed

Problem Statement

Let P(x,y) P(x,y) be a polynomial in two variables x,y x,y such that P(x,y)\equal{}P(y,x) for every x,y x,y (for example, the polynomial x^2\minus{}2xy\plus{}y^2 satisfies this condition). Given that (x\minus{}y) is a factor of P(x,y) P(x,y), show that (x\minus{}y)^2 is a factor of P(x,y) P(x,y).
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