Abstract
It is proved that if 1 <c < 97 , then the Diophantine inequality |p c +p c +p c + p cN| < log �1 N is solvable in prime numbers p1,p2,p3,p4 for sufficiently large real number N. This result constitutes an improvement upon that of Zhai and Cao for the range 1 <c< 81 .
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