Abstract
Let 1<c<11/10. In the present paper it is proved that there exists a numberN(c)>0 such that for each real numberN>N(c) the inequality\(|p_1^c + p_2^c + p_3^c - N|< N^{ - \tfrac{1}{c}(\tfrac{{11}}{{10}} - c)} \log ^{c_1 } N\) is solvable in prime numbersp 1,p 2,p 3, wherec 1 is some absolute positive constant.
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Project supported by the National Natural Science Foundation of China (grant: 19801021) and by MCSEC
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Cai, Y. On a diophantine inequality involving prime numbers (III). Acta Mathematica Sinica 15, 387–394 (1999). https://doi.org/10.1007/BF02650733
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DOI: https://doi.org/10.1007/BF02650733