5

Part of 2007 QEDMO 5th

Problems(1)

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

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

a

b

c

be three integers. Prove that there exist six integers

x

y

z

x^{\prime}

y^{\prime}

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}.

inductionalgebrafunctiondomaincalculusintegrationpolynomial