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In this note we find all the solutions to the equation  x  2  + 2  α   3  β   19  γ   =  y n   in nonnegative unknowns with  n  ≥ 3 and gcd( x ,  y ) = 1, and nonnegative solutions to  x  2  + 2  α   3  β   13  γ   =  y n   with  n  ≥ 3, gcd( x ,  y ) = 1, except when  α  = 0 and  x .  β .  γ  is odd.

On the Diophantine equations x 2 + 2 α 3 β 19 γ = y n and x 2 + 2 α 3 β 13 γ = y n