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

Abstract

In this paper, it is proved that every pair of sufficiently large even integers can be represented by a pair of equations, each containing one prime, one prime square, two prime cubes and 302 powers of 2. This result constitutes a refinement upon that of L. Q. Hu and L. Yang. Mathematical subject classification (2010). 11P32, 11P55. Manuscript received 19th December 2019, revised 9th February 2020 and 10th February 2020, accepted 10th February 2020.