MathDB

Let

\mathbb{A} \subset \mathbb{N}

such that all elements in

\mathbb{A}

can be representable in the form of

x^2+2y^2

x,y \in \mathbb{N}

, and

x>y

. Let

\mathbb{B} \subset \mathbb{N}

such that all elements in

\mathbb{B}

can be representable in the form of

\displaystyle \frac{a^3+b^3+c^3}{a+b+c}

a,b,c \in \mathbb{N}

, and

a,b,c

are distinct.
a) Prove that

\mathbb{A} \subset \mathbb{B}

.
b) Prove that there exist infinitely many positive integers

n

satisfy

n \in \mathbb{B}

and

n \not \in \mathbb{A}

Problem Statement