Pythagorean Triples

[mossy ether]

I've been recently invested in the idea of primitive pythagorean triples.
After a bit of investigation, I learned that the hypotenuse of the triangle must be m^2 + n^2 where m and n are distinct natural numbers, and m^2 + n^2 and m^2 - n^2 are coprime.
I was wondering whether the recipicoral sum would be something interesting or whether it would diverge. Namely:
1/5 + 1/13 + 1/17 + 1/25 + 1/29 +...

[elfin seal]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations
4. Do not ping the mods, unless someone is breaking the rules.
5. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[crude gazelle]

all reciprocals of hypotenuses?

[mossy ether]

yeah im pretty sure it diverges anyways

[delicate blaze]

You might find this interesting:

https://youtu.be/QJYmyhnaaek?si=QQIzbsjarecLw__q

[mossy ether]

yeah i saw that

3blue1brown is great

[balmy flame]

Here’s a really interesting thing with Pythagorean triples. U’ll have to watch it from the start https://youtu.be/0pz-keCwC3k?si=s1PgvssQukCm1vj4

It starts of seeming unrelated to pythag triples

But then u find that they come into it and it’s a weird pattern

[scenic crater]

yep it does

if you choose the larger of m,n to be an odd prime p, then (p,2), (p,4), ..., (p,p-1) are all valid
the sum of those is at least (p-1)/(2*2p^2) which diverges