MathDB
a = yz' - zy', b = zx' - xz', c = xy' - yx'

Source: 5th QEDMO problem 5, coming from ring theory but turning out unexpectedly easy

November 10, 2007
inductionalgebrafunctiondomaincalculusintegrationpolynomial

Problem Statement

Let a a, b b, c c be three integers. Prove that there exist six integers x x, y y, z z, x′ x^{\prime}, y′ y^{\prime}, z′ z^{\prime} such that a\equal{}yz^{\prime}\minus{}zy^{\prime};\ \ \ \ \ \ \ \ \ \ b\equal{}zx^{\prime}\minus{}xz^{\prime};\ \ \ \ \ \ \ \ \ \ c\equal{}xy^{\prime}\minus{}yx^{\prime}.
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