MathDB

Let

M

be the set of all integers in the form of

a^2+13b^2

, where

a

and

b

are distinct itnegers.
i) Prove that the product of any two elements of

M

is also an element of

M

.
ii) Determine, reasonably, if there exist infinite pairs of integers

(x,y)

so that

x+y\not\in M

but

x^{13}+y^{13}\in M

Problem Statement