Let $R$ be a prime ring with center $Z$ and $f\ne 0$ a right generalized $(\alpha,\beta)$-derivation of $R$. If $f(x)^n\in Z$ for all $x\in L$, a nonzero ideal of $R$, and for some fixed positive integer $n$, then $R$ is either commutative or is an order in a $4$-dimensional simple algebra.
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