MathDB

Call admissible a set

A

of integers that has the following property: If

x,y \in A

(possibly

x=y

) then

x^2+kxy+y^2 \in A

for every integer

k

. Determine all pairs

m,n

of nonzero integers such that the only admissible set containing both

m

and

n

is the set of all integers.
Proposed by Warut Suksompong, Thailand

Problem Statement