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Paper   IPM / M / 15537
School of Mathematics
  Title:   On the diophantine equations X2+2\Alpha 3\Beta 19Γ=YN and X2+2\Alpha 3\Beta 13Γ=YN
  Author(s):  Amir Ghadermarzi
  Status:   Published
  Journal: Math. Slovaca
  Vol.:  69
  Year:  2019
  Pages:   507-520
  Supported by:  IPM
  Abstract:
In this note we find all the solutions to the equation x2+2α 3β 19γ=yn in nonnegative unknowns with n ≥ 3 and gcd(x,y)=1, and nonnegative solutions to x2+2α 3β 13γ=yn with n ≥ 3 , gcd(x,y)=1, except when α = 0 and x. β. γ is odd.

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