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If $f$ and $g$ are odd functions, we prove, in this paper, that the Abel equation has a center at the origin. We also consider a class of polynomial differential equations $\\dot{x} = -y+P_n(x,y)$ and $\\dot{y} = x+Q_n(x,y)$, where $P_n$ and $Q_n$ are homogeneous polynomials of degree $n$. 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