5 is good, 2005 is better, and 2005^2 is best Puerto Rico Ibero IMO TST 2009.1
Source:
September 16, 2021
number theory
Problem Statement
A positive integer is called good if it can be written as the sum of two distinct integer squares. A positive integer is called better if it can be written in at least two was as the sum of two integer squares. A positive integer is called best if it can be written in at least four ways as the sum of two distinct integer squares.
a) Prove that the product of two good numbers is good.
b) Prove that is good, is better, and is best.