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) =… Click to show full abstract
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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