On a Diophantine equation with prime numbers

摘要

Let [0] denote the integral part of the real number 0. In this paper, it is proved that for 2 < c < 408/197, the Diophantine equation [p(1)(c)] + [p(2)(c)] + [p(3)(c)] + [p(4)(c)] + [p(5)(c)] = N is solvable in prime variables p(1), . . . , p(5) for sufficiently large integer N.