Let \(2< c < \frac{52}{25}\). In this paper, it is proved that for any sufficiently large real number N, the Diophantine inequality \(|p_1^{c} + p_2^{c} + p_3^{c} + p_4^{c} + p_5^{c} - N|< N^{-\frac{9}{10c}(\frac{52}{25}-c)}\) is solvable in primes \(p_1,\cdots ,p_5\). This result constitutes an improvement upon that of Baker and Weingartner.

中文翻译：

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关于涉及素数的丢番图不等式

令\（2 <c <\ frac {52} {25} \）。本文证明，对于任何足够大的实数N，Diophantine不等式\（| p_1 ^ {c} + p_2 ^ {c} + p_3 ^ {c} + p_4 ^ {c} + p_5 ^ {c }-N | <N ^ {-\ frac {9} {10c}（\ frac {52} {25} -c）} \）可解质数\（p_1，\ cdots，p_5 \）。该结果构成了对Baker和Weingartner的改进。