Browsing by Author "Miyazaki, Takafumi"

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    On the Diophantine equation ((c+1)m2+1)x + (cm2-1)y = (am)z
    (Bilimsel ve Teknolojik Araştırma Kurumu, 2018-08-10) Miyazaki, Takafumi; Kızıldere, Elif; Soydan, Gökhan; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 0000-0002-6321-4132; 0000-0002-7651-7001; M-9459-2017; 57204173004; 23566953200
    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.