An additive equation involving fractional powers

Let 1 < c < 14/11 and N be a sufficiently large integer. We prove that almost all n is an element of (N, 2N] can be represented as n = [p(1)(c)] + [p(2)(c)], where p(1), p(2) are prime numbers and [x] denotes the integer part of x. Our method also yields an asymptotic formula for the number of representations of these n. The range 1 < c < 14/11 constitutes an extension of 1 < c < 17/16 due to Laporta.