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Namely, let $a\\in R$, then $a$ is EP if and only if there exists $x\\in R$ such that $(xa)^{\\ast}=xa$, $xa^{2}=a$ and $ax^{2}=x.$ It is well known that all EP elements in $R$ are core invertible and Moore-Penrose invertible. We give more equivalent conditions for a core (Moore-Penrose) invertible element to be an EP element. 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