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We prove that a Finsler manifold with vanishing Berwald scalar curvature has zero E-curvature.As a consequence,Landsberg manifolds with vanishing Berwald scalar curvature are Berwald manifolds.For (α,β)-metrics on manifold of dimension greater than 2,if the mean Landsberg curvature and the Berwald scalar curvature both vanish,then the Berwald curvature also vanishes.