On the exponential Diophantine equation m(x) + (m+1)(y) = (1+m plus m(2))(z)

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ALAN M.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.29, sa.3, ss.23-32, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.2478/auom-2021-0032
  • Dergi Adı: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Sayfa Sayıları: ss.23-32
  • Anahtar Kelimeler: exponential Diophantine equations, Classification Method, primitive divisor theorem, JESMANOWICZ CONJECTURE, DIVISORS
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Let m > 1 be a positive integer. We show that the exponential Diophantine equation m(x) + (m + 1)(y) = (1 + m + m(2))(z) has only the positive integer solution (x, y, z) = (2, 1, 1) when m >= 2.