All big integers can be expressed as the sum of maximally seven primes

On the Representation of Even Integers as Sum of Two Almost Equal Primes

In this paper we generalize the Chudakov van der Corput Estermann Theorem on the exceptional set in the binary Goldbach problem to a result on the same problem with "almost equal" primes. Actually, we prove that the equation Pi +P2 = 2n is satisfied by almost ali 2ra € [N, 2N] when the primes pi and p-2 lie in the interval [n — U, n + U], with U = n^. Furthermore, we explicitly estimate the num...

When a Boolean Function can be Expressed as the Sum of two Bent Functions

In this paper we study the problem that when a Boolean function can be represented as the sum of two bent functions. This problem was recently presented by N. Tokareva in studying the number of bent functions [20]. Firstly, many functions, such as quadratic Boolean functions, MaioranaMacFarland bent functions, partial spread functions etc, are proved to be able to be represented as the sum of t...

Can a single floating body be expressed as the sum of two bodies ?

Integers Represented as a Sum of Primes and Powers of Two

It was shown by Linnik [10] that there is an absolute constant K such that every sufficiently large even integer can be written as a sum of two primes and at most K powers of two. This is a remarkably strong approximation to the Goldbach Conjecture. It gives us a very explicit set K(x) of integers n ≤ x of cardinality only O((log x)), such that every sufficiently large even integer N ≤ x can be...

Representations of Integers as the Sum of k Terms

Let A = {a1, a2, . . . } (a1 < a2 < . . . ) be a xed in nite sequence of positive integers, and let Rk(n) denote the number of solutions of ai1 + ai2 + · · · + aik = n, ai1 ∈ A, . . . , aik ∈ A. For k = 2, P. Erd®s and A. Sárközy proved if F (n) is a nice arithmetic function then there exists a sequence A such that |R2(n)−F (n)| (F (n) log n)1/2. The aim of this paper is to extend their result ...