Powers of 2 in two Goldbach-Linnik type problems involving prime cubes.

In this paper, we show that every sufficiently large even integer can be represented as eight prime cubes and k 1 powers of 2, and every pair of sufficiently large even integers can be represented as a pair of eight prime cubes and k 2 powers of 2, where k 1 = 28 and k 2 = 98. These results improve previous results k 1 = 30 and k 2 = 335 , respectively. [ABSTRACT FROM AUTHOR]