MathDB

Let

A

be a non-empty subset of the set of all positive integers

N^*

. If any sufficient big positive integer can be expressed as the sum of

2

elements in

A

(The two integers do not have to be different), then we call that

A

is a divalent radical. For

x \geq 1

, let

A(x)

be the set of all elements in

A

that do not exceed

x

, prove that there exist a divalent radical

A

and a constant number

C

so that for every

x \geq 1

, there is always

\left| A(x) \right| \leq C \sqrt{x}

Problem Statement