Squares of Primes and Powers of 2, II Original Research Article

We prove that the density of integers ≡2 (mod 24), which can be represented as the sum of two squares of primes and k powers of 4, tends to 1 as k→∞ in the sequence k≡0 (mod 3). Consequently, there exists a positive integer k0 such that every large integer ≡4 (mod 24) is the sum of four squares of primes and k0 powers of 4.