The Diophantine equation $(bn)^{x}+(2n)^{y}=((b+2)n)^{z}$

Volume 132 / 2013

Min Tang, Quan-Hui Yang Colloquium Mathematicum 132 (2013), 95-100 MSC: Primary 11D61. DOI: 10.4064/cm132-1-7


Recently, Miyazaki and Togbé proved that for any fixed odd integer $b\geq 5$ with $b\not =89$, the Diophantine equation $b^{x}+2^{y}=(b+2)^{z}$ has only the solution $(x,y,z)=(1,1,1)$. We give an extension of this result.


  • Min TangDepartment of Mathematics
    Anhui Normal University
    Wuhu 241003, China
  • Quan-Hui YangSchool of Mathematical Sciences
    Nanjing Normal University
    Nanjing 210023, China

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