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In this paper we study in natural numbers some diophantine equa-tion of ax + by = z2 type. 2000 Mathematical Subject Classification: 11D61 In this note we study diophantine equation of ax + by = z2 type, where a, b, c ∈ N∗, a, b ≥ 2, a 6 = b. In their study we use the method of modular arithmetics. 1. Equation 2x + 7y = z2. We have the following result: Proposition 1.1. The diophantine equation 2x + 7y = z2 has exactly three solutions (x, y, z) ∈ {(3, 0, 3), (5, 2, 9), (1, 1, 2)}. Proof. We consider several cases. Case 1.1. For x = 0, then we have the diophantine equation 7y = z2 −