On the Diophantine equation ((c+1)m(2)+1)(x) + (cm(2)-1)(y) = (am)(z)


Kizildere E., Miyazaki T., SOYDAN G.

TURKISH JOURNAL OF MATHEMATICS, vol.42, no.5, pp.2690-2698, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 5
  • Publication Date: 2018
  • Doi Number: 10.3906/mat-1803-14
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.2690-2698
  • Keywords: Exponential Diophantine equation, Jacobi symbol, lower bound for linear forms in logarithms, LINEAR-FORMS, 2 LOGARITHMS, CONJECTURE

Abstract

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.