MathDB

30

Part of 1971 IMO Longlists

Problems(1)

There cannot be 5 distinct solutions [ILL 1971]

Source:

1/1/2011
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?
parameterizationalgebrasystem of equationsalgebra proposed