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Our main goal is to show that if there exist Jordan derivations D and G on a noncommutative (n + 1)!-torsion free prime ring R such that for all x ∈ R, then we have D = 0 and G = 0. We also prove that if there exists a derivation D on a noncommutative 2-torsion free prime ring R such that the mapping x → [aD(x), x] is commuting on R, then we have either a = 0 or D = 0.doi:10.4134/bkms.2002.39.4.635 fatcat:6igadhvkjbgsxnv7iqwcrqe7da