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A note on the Diophantine equation $\left( {m^3 - 3m} \right)^x + \left( {3m^2 - 1} \right)^y = \left( {m^2 + 1} \right)^z$
Let m be a positive integer.In this note, using some elementary methods, we prove that if 211m, 3rn 2-1 is an odd prime, then the equation (rn 3-3m) x + (3m 2-1) (rn + 1) has only the positive integer solution (:c, y, z) (2, 2, 3).