A Cauchy-Type Functional Inequality for the Error Function

Integers expressible as sums of primes and composites

“…However, Zhang's techniques from [8] can only be directly applied to odd integers so as to obtain the following inequivalent result: every odd integer greater than 23 can be represented in the form p C q C c, where p and q are prime and c is a composite number such that p, q, and c are pairwise coprime. Furthermore, it appears that the only research, apart from our current note, currently citing Zhang's work in [8] is due to Alzer and Kwong [1], who did not introduce any results on or related to the expression of integers in the form p C c in the manner we have previously indicated. We succeed, as below, in proving that Zhang's result also holds for odd integers.…”

“…equals 2N 2 . The integer set in (1) seems like a natural variant of (3), and since Zhang [8] has shown that 2N 16 is contained in (1), this leads us to consider something of a variant of the Goldbach conjecture for odd integers, as in the problem of expressing odd integers in the form indicated in (1). Let !.n/ denote the number of distinct prime factors of n. Let .n/ denote the primecounting function giving the number of primes less than or equal to n. Zhang, in 2020 [8] for n 60184 (see [2]), together with the inequality proved by Robin [6] whereby…”