Miyazaki, Takafumi2024-01-092024-01-092018-08-10Kızıldere, E. vd. (2018). ''On the Diophantine equation ((c+1)m2+1)x + (cm2-1)y = (am)z''. Turkish Journal of Mathematics, 42(5), 2690-2698.1300-00981303-6149https://doi.org/10.3906/mat-1803-14https://journals.tubitak.gov.tr/math/vol42/iss5/45/https://hdl.handle.net/11452/38884Suppose that c, in, and a are positive integers with a 11, 13 (mod 24) . In this work, we prove that when 2c + 1 = a(2), the Diophantine equation in the title has only solution (x, y, z) = (1,1,2) where m +/- 1 (mod a) and m > a(2) in positive integers. The main tools of the proofs are elementary methods and Baker's theory.eninfo:eu-repo/semantics/closedAccessMathematicsExponential diophantine equationJacobi symbolLower bound for linear forms in logarithmsLinear-forms2 logarithmsConjectureArticle0004479468000462-s2.0-8505478598926902698425MathematicsDiophantine Equation; Number; Linear Forms in Logarithms