Kızıldere, Elifle, MaohuaSoydan, Gökhan2024-07-242024-07-242020-06-010081-6906https://doi.org/10.1556/012.2020.57.2.1457https://akjournals.com/view/journals/012/57/2/article-p200.xmlhttps://hdl.handle.net/11452/43396Let l,m,r be fixed positive integers such that 2 vertical bar l, 3 lm, l > r and 3 vertical bar r. In this paper, using the BHV theorem on the existence of primitive divisors of Lehmer numbers, we prove that if min{rlm(2) - 1,(l-r)lm(2) + 1} >30, then the equation (rlm(2) - 1)(x) + ((l - r)lm(2) + 1)(y) = (lm)(z) only the positive integer solution (x,y,z) = (1,1,2).eninfo:eu-repo/semantics/closedAccessTernary purely exponential diophantine equationBhv theorem on the existence of primitive divisors of lehmer numbersScience & technologyPhysical sciencesMathematicsArticle00057097840000620020557210.1556/012.2020.57.2.14571588-2896