On the exponential Diophantine equation (18m(2 )+1)(x) + (7m(2)-1)(y) = (5m)(z)

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ALAN M.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.4, ss.1990-1999, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 4
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1801-76
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1990-1999
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Let m be a positive integer. We show that the exponential Diophantine equation (18m(2) + 1)(x) + (7m(2) - 1)(y) = (5m)(z) has only the positive integer solution (x, y, z) = (1, 1, 2) except for m 23, 47, 63, 87 (mod 120) . For m not equivalent to 0 (mod 5) we use some elementary methods and linear forms in two logarithms. For m 0 (mod 5) we apply a result for linear forms in p-adic logarithms.