On pairs of equations in unlike powers of primes and powers of 2

Abstract

Abstract:In this paper, we obtained that when k = , every pair of large even integers satisfying some necessary conditions can be represented in the form of a pair of unlike powers of primes and k powers of .

On pairs of one prime, four prime cubes and powers of 2

“…He proved that the equations (1.5) are solvable for k = 332, and then the consequence was advanced by Hu and Yang [3] for k 2 = 128. In 2017, Hu and Yang [4] proved every pair of large integers with N 2 ≫ N 1 ≥ N 2 can be represented in the form…”

On pairs of equations involving unlike powers of primes and powers of 2

“…where k is a positive integer. In 2017, Hu and Yang [1] proved that for k = 455, the equations (5) are solvable. In this paper, we obtain a further improvement of the value of k by giving the following theorem.…”