Set and set builder notation

Question

I have this following set notation:

$$ \{n \in \mathbb Z | n = k^2 + l^2\text{ for some integers }k\text{ and }l\} $$ I don't know if $k$ and $l$ have to be equal for each pair of integers. Or they could be any value?

I would appreciate any help.

My current solution is $\{0,2,8,18,32,50,72,98,\ldots\}$.

Answer 1

No, we cannot write $3$ as the sum of two squares. We can only write $3$ as the sum of non negative integers in two ways: $1 + 2$ and $0 + 3$, and neither are the sum of squares.

If you're looking for the elements of that set: https://wstein.org/edu/Fall2001/124/lectures/lecture21/lecture21/node2.html

Answer 2

I see no reason why $k$ and $l$ should be equal, so you're missing quite a few numbers from the set.