Le, Maohua2024-01-152024-01-152019-07-11Le, M. ve Soydan, G. (2020). "An application of Baker’s method to the Jeśmanowicz’ conjecture on primitive Pythagorean triples". Periodica Mathematica Hungarica, 80(1), 74-80.0031-53031588-2829https://doi.org/10.1007/s10998-019-00295-0https://link.springer.com/article/10.1007/s10998-019-00295-0https://hdl.handle.net/11452/39031Let m, n be positive integers such that m > n, gcd(m,n) = 1 and m not equivalent to n(mod2) . In 1956, L. Jesmanowicz conjectured that the equation (m(2)-n(2))(x) + (2mn)(y) = (m(2) + n(2))(z) has only the positive integer solution (x,y,z)=(2,2,2). This conjecture is still unsolved. In this paper, combining a lower bound for linear forms in two logarithms due to M. Laurent with some elementary methods, we prove that if mn equivalent to 2(mod 4) and m > 30.8n, then Jesmanowicz' conjecture is true.eninfo:eu-repo/semantics/closedAccessMathematicsTernary purely exponential Diophantine equationPrimitive Pythagorean tripleJesmanowicz' conjectureApplication of Baker's methodArticle0005119989000062-s2.0-850689025337480801Mathematics, appliedMathematicsDiophantine Equation; Number; Linear Forms in Logarithms