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, vol.29, no.3, pp.23-32, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.2478/auom-2021-0032
  • Journal Name: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH, Directory of Open Access Journals
  • Page Numbers: pp.23-32
  • Keywords: exponential Diophantine equations, Classification Method, primitive divisor theorem, JESMANOWICZ CONJECTURE, DIVISORS
  • Yıldız Technical University Affiliated: Yes

Abstract

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.