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, cilt.42, sa.5, ss.2690-2698, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 5
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1803-14
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.2690-2698
  • Anahtar Kelimeler: Exponential Diophantine equation, Jacobi symbol, lower bound for linear forms in logarithms, LINEAR-FORMS, 2 LOGARITHMS, CONJECTURE
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.