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Let $\lambda B_{p}$, where $\lambda$ is a nonzero complex number, denote aconstant-weighted backward shift operators on $l^{p}$ for $1\leq p<\infty$. Inthis article, we investigate, in topologically conjugacy, the completeclassification for $\lambda B_{p}$.

$2B_{p}$ and $4B_{p}$ are topologically conjugate