The set of equations I am using are 6xy+x+y, 6xy+x-y, 6xy-x+y, 6xy-x-y.

When counting numbers (1,2,3...) are put into the equations counting numbers are returned. There are however some numbers that cannot be returned regardless of the input number.

What I am trying to prove is whether or not the set of impossible numbers is finite or infinite.

Any help with a proof would be appreciated