- #1

- 29

- 4

(1) Four of them are 0+5

*i*, 0-5

*i,*and 5+0i, -5+0i. They lie on the orthogonal (real and imaginary) axes.

(2) The other eight are 3+4i, 3-4i, -3+4i, -3-4i, 4+3i, 4-3i, -4+3i and -4-3i. These do not lie on the orthogonal axes.

Each of these twelve integers is the product of two integers with norm 5, but it matters which ones.

If there are any insights as to these kinds of Gaussian integers (having different symmetries but the same norm), I would appreciate any thoughts. Also, I assume these become more numerous as norms get larger?

Thanks!

-Jeffrey