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MR909837 (89d:11023) 11D68 (11A05)
Cao, Zhen Fu; Liu, Rui; Zhang, Liang Rui On the equation $\sum\sp s\sb {j=1}(1/x\sb j)+(1/(x\sb 1\cdots x\sb s))=1$ and Znám's problem. J. Number Theory 27 (1987), no. 2, 206–211.
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