MathDB
There cannot be 5 distinct solutions [ILL 1971]

Source:

January 1, 2011
parameterizationalgebrasystem of equationsalgebra proposed

Problem Statement

Prove that the system of equations 2yz+x−y−z=a,2xz−x+y−z=a,2xy−x−y+z=a,2yz+x-y-z=a,\\ 2xz-x+y-z=a,\\ 2xy-x-y+z=a, aa being a parameter, cannot have five distinct solutions. For what values of aa does this system have four distinct integer solutions?
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