Kızıldere, ElifSoydan, Gökhan2024-07-052024-07-052020-03-011225-293Xhttps://doi.org/10.5831/HMJ.2020.42.1.139http://koreascience.or.kr/article/JAKO202009444381938.pagehttps://hdl.handle.net/11452/42971Let 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 (5pn(2) - 1)(x) + (p(p - 5)n(2) + 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 (35n(2) - 1)(x) + (14n(2) + 1)(y) = (7n)(z) has only the positive integer solution (x, y, z) = (1; 1; 2) where n +/- 3 (mod 5) or 5 vertical bar n. On the proofs, we use the properties of Jacobi symbol and Baker's method.eninfo:eu-repo/semantics/closedAccessLinear-forms2 logarithmsConjectureExponential diophantine equationJacobi symbolBaker's methodScience & technologyPhysical sciencesMathematicsArticle00052359200001013915042110.5831/HMJ.2020.42.1.1392288-6176