For v = 0, we get 2x−y − 1 = 2. It is impossible.
For v = 1, we have 2x−y−2 − 1 = 1. So, 2x−y−2 = 2. That is x − y − 2 = 1. Then
we get x = 2k + 3 and a = 3. Hence, the solution of the diophantine equation (1) is
(x, y, z) = (2k + 3, 2k, 3 · 2
k
) where k is a non-negative integer.