On the Diophantine equation $x^2 + 2^{\alpha} 13^{\beta}= y^{n}$

Volume 116 / 2009

Florian Luca, Alain Togbé Colloquium Mathematicum 116 (2009), 139-146 MSC: 11D61, 11Y50. DOI: 10.4064/cm116-1-7


We find all the solutions of the Diophantine equation $$x^2 + 2^{\alpha} 13^{\beta}= y^n$$ in positive integers $x,y,\alpha,\beta,n\ge 3$ with $x$ and $y$ coprime.


  • Florian LucaInstituto de Matemáticas UNAM
    Campus Morelia
    Apartado Postal 27-3 (Xangari)
    C.P. 58089
    Morelia, Michoacán, Mexico
  • Alain TogbéMathematics Department
    Purdue University North Central
    1401 S, U.S. 421
    Westville, IN 46391 U.S.A.

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