Number authority is from the knowledge embedded in numbers which is infinite and absolute. Like consider:
12 + 32 = 10
82 + 62 = 102
262 + 182 = 103
282 + 962 = 104
3162 + 362 = 105
So yeah, every power of 10 out to infinity is a sum of two squares, which doesn't seem useful to me, just curious. What can it tell me? Such things I enjoy pondering though yeah, also just like looking at numbers as you may have noticed.
Am just using a specific of a more general result as 10 is such a big deal to many, including me.
The numbers KNOW and we can find things out, if we want. So much depends though, on asking questions. The numbers know infinite information. We can find some things out.
If it doesn't interest you, ok.
For me such things DO interest, and this result follows from a simple rule.
If: u2 + 9v2 = 10a
Then: (u - 9v)2 + 9(u + v)2 = 10a+1
Which is just using my BQD Iterator. And notice that u and v can be positive or negative, while I like to show positive as is easier and looks prettier. Copied much from an earlier post where you can go there to read more.
And there are LOTS of posts on my BQD Iterator, and you can find a list of those I've labeled by clicking on label beneath this post.