Proof: The case when x = 0 and z = 0 are obvious. So,
we only consider the case when x, z > 0. Hence, (z + 1)(z −
1) = 3x. It follows that 2 = (z + 1) − (z − 1) = 3β − 3α
where α + β = x and β > α. This implies that α = 0 and
3x − 1 = 2 or equivalently 3x = 31. Thus, x = 1 and z = 2