Goldbach-Linnik Type Problems Involving Unequal Powers Of Primes And Powers Of Two

In this thesis,it is proved that every pair of sufficiently large even integers can be represented as not only a pair of one prime,one prime square,one prime cube,one prime biquadrate and 70 powers of 2,such that where k1=70,but also a pair of two squares of primes,two cubes of primes,two fourth powers of primes and 66 powers of 2,such that where k2=66.