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We obtain similar types of conclusions as that of Brück 3 for two differential polynomials which in turn radically improve and generalize several existing results. Moreover a number of examples have been exhibited to justify the necessity or sharpness of some conditions used in the paper. At last we pose an open problem for future research.doi:10.4134/ckms.2016.31.2.311 fatcat:cylpsskbzfa6tmku73qhuj45a4