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Let p be a prime number with p > 3, p ≡ 3 (mod 4) and let n be a positive integer. In this paper, we prove that the Diophantine equation (5pn2 - 1)x + (p(p - 5)n2 + 1)y = (pn)z has only the positive integer solution (x, y, z) = (1, 1, 2) where pn ≡ ±1 (mod 5). As an another result, we show that the Diophantine equation (35n2 - 1)x + (14n2 + 1)y = (7n)z has only the positive integer solution (x, y, z) = (1, 1, 2) where n ≡ ±3 (mod 5) or 5 | n. On the proofs, we use the properties of Jacobi symbol and Baker's method.
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