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The theory predicts that the effect of gravitational lensing by the matterassociated with clusters of galaxies can magnify background sources, leading toan enhancement of source number density around foreground clusters of galaxies.We conduct a search for the associations of distant radio-bright quasars withAbell clusters using the 1-Jy and 2-Jy all-sky catalogs. Statistics turns to bevery poor on the basis of the 1-Jy sample, which shows no correlations betweenthe distant radio quasars with the foreground Abell clusters above $1\sigma$level. However, an apparent association ($>1\sigma$) of the 2-Jy radio sourceswith the foreground Abell clusters has been detected on scale of $\sim20$arcminutes. We point out that this enhancement is unlikely to be produced bythe statistical gravitational lensing hypothesis utilizing the matterassociated with a population of isolated clusters unless (1)their velocitydispersion is a few times larger than the presently adopted value and/or (2)theintrinsic counts of the radio-bright sources with flux have a steeper slopethan the presently observed ones. This indicates that (1)the observedassociations, if real, can be the integrated result of all the matter along theline of sight to the distant quasars, namely, the weak lensing effect ofclusters of galaxies that trace large-scale structures of the universe, and/or(2)the number counts of the radio-bright sources have been seriouslycontaminated by lensing.Comment: 10 pages Latex style, 3 figures available on request from X.P. Wu  (wxp@bao01.bao.ac.cn), MNRAS in pres

A search for associations of distant radio-bright quasars with Abell clusters: an effect of gravitational amplification bias?