In number theory the Diophantine equations are studied, equations in which only integer solutions are permitted. The famous general equation ax +by = z2 has many forms. The literature contains a very large number of articles on non-linear such individual equations [1–6]. In this paper, we solve the equation 2x + 33y = z2, where x; y; z are nonnegative integer numbers. Theorem. The Diophantine equation 2x + 33y = z2 has exactly three nonnegative integer solutions: (x; y; z) 2 f(3; 0; 3); (4; 1; 7); (8; 1; 17)g.