Statement If axby cz d has an integer solution then axby d has an integer solution Disproof As a counterexample consider a b c 2 and d 1 We claim that ax by d does not have a solution To show this suppose it did Then there would exist integers x0 and y0 such that 2x0 2y0 1 This is a contradiction because 2x0 y0 is even and one is odd