TURKISH JOURNAL OF MATHEMATICS, vol.42, no.5, pp.2690-2698, 2018 (SCI-Expanded)
Article / Article
TURKISH JOURNAL OF MATHEMATICS
Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
Exponential Diophantine equation, Jacobi symbol, lower bound for linear forms in logarithms, LINEAR-FORMS, 2 LOGARITHMS, CONJECTURE
Bursa Uludag University Affiliated:
Suppose 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.