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diophantine system, xyzu-x^3=9 , x+yz=3/2 u

Source: 2007 Swedish Mathematical Competition p1

April 27, 2021
number theoryDiophantine equationsystem of equationsdiophantine

Problem Statement

Solve the following system {xyzu−x3=9x+yz=32u \left\{ \begin{array}{l} xyzu-x^3=9 \\ x+yz=\dfrac{3}{2}u \\ \end{array} \right. in positive integers xx, yy, zz and uu.
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