Exceptional Set in Waring–Goldbach Problem Involving Squares, Cubes and Sixth Powers.

Let N be a sufficiently large integer. In this paper, it is proved that, with at most O(N^119/270+s) exceptions, all even positive integers up to N can be represented in the form p 1 2 + p 2 2 + p 3 3 + p 4 3 + p 5 6 + p 6 6 , where p₁, p₂, p₃, p₄, p₅, p₆ are prime numbers. [ABSTRACT FROM AUTHOR]