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There exists the rational numbers u,v,w

Source: IberoAmerican 1988 Q5

December 13, 2010
quadraticsalgebrasystem of equationsalgebra proposed

Problem Statement

Consider all the numbers of the form x+yt+zt2x+yt+zt^2, with x,y,zx,y,z rational numbers and t=23t=\sqrt[3]{2}. Prove that if x+yt+zt2≠0x+yt+zt^2\not= 0, then there exist rational numbers u,v,wu,v,w such that (x+yt+z2)(u+vt+wt2)=1(x+yt+z^2)(u+vt+wt^2)=1
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