A Short Note on Two Diophantine Equations 9 x – 3y = z2 and 13x – 7y = z2

In this short note, we show that the Diophantine equation 2 9 3 x y − = z has all non-negative integer solutions, , ∈, 2, 0: ∈ ℕ ∪ {0} and the Diophantine equation 2 13 7 x y − = z have the unique non-negative integer solution (, , ) (0, 0, 0) x y z =.