I think I got the idea, I just now updated the original post and added a footnote how I understood the Brahmagupta–Fibonacci identity.
I have only surface knowledge about imaginary numbers, but I have noticed sum of two squares being also referred as Gaussian integers.
There’s definitely a lot of material to read about relating both Gaussian integers and Pythagorean triples, that I can gain intuition how all of these relations work out. I much appreciate the help!

Thank you for the answer! I have to take deeper look into that.
It’s rather interesting how seemingly two different sum components share factors. It’s like finding pi from seemingly unrelated series.

After some thinking I came up with this.
Conjecture:

N² = a²+b²
N  = c²+d²

a = 2*c*d
b = d²-c²

integers a,b,c,d>0

For any integer N that can be expressed as both N²=a²+b² and N=c²+d², the relationship a=2*c*d holds.  

Is it enough proof just to show that the above equations are true when substituting them to N² and N equations?
If a = 2*c*d then one leg of the Pythagorean triple definitely contains c and d factors and ‘2’. This might be related to Pythagorean triple parametrization.

I fixed the flawed ChatGPT counterexample finder script and now it gives this list of all numbers including composites which don’t follow these rules, such as 58. Here’s sub-sequence of A004431 numbers that don’t follow the rules:

Numbers which neither Pythagorean side is divisible by 4
Composites: [10, 26, 34, 50, 58, 74, 82, 90, 106, 122, 130, 146, 170, 178...]
This is identical to Sums of two distinct odd squares A339977 which makes sense as if c,d>1 and odd, they must be 3 or bigger hence their factors are missing the extra ‘2’, unlike primes where one of c or d is always even.
Even composites appear to follow a=2*c*d relation. The prime pythagorean side divisibility by 4 appears to be just a side effect.

That’s what 65dos Taipei music video looks like, though that was released 2013 https://youtu.be/06ObT5yIIx8

So it’s illegal to die poor

I just have it in muscle memory to know which way soda bottle cap tightens

I genuinely thought symlinking these files was standard because how many people I have seen suggesting it. I have had this issue so many times when I needed to that one program updated but there’s no newer libraries in AUR. Surprisingly, I haven’t had issues and I’ve been doing this past 5 years on my personal system. So I guess I consider compiling from source next time.

It did brush my mind as I’m still baffled about some abortion laws even if there’s no brain development. But if it was an egg, it would be hard to enforce it and some eggs aren’t fertilized. I bet someone would try to outlaw having a miscarriage if they could.

The more you know. So it could be more likely that humans sat on their eggs to keep them warm, or they would have been limited to tropical climates. Humans would have evolved very differently regardless.

Yes, my parents used to have chickens. It’s unlikely that the incubation period would be 9 months and being oviparous has It’s own challenges. If humans did evolve that route I’d imagine that we’d have overcome most of the issues. Dinosaurs being one example, it’s possible humans would be cold blooded and have learned the joy of regurgitation. It comes down to speculation whether human like intelligence could have evolved with these limitations.

Dinosaurs were pretty big too

Once the phone runs out of battery, send it to warranty repair

One more reason to subscribe to float plane

this took me a while but after converting to ascii in hex I get it

“())(” = 40 41 41 40

“()()” = 40 41 40 41

As long your strings aren’t null terminated

I later figured that pkill -9 -f "\.exe" works if wineserver -k doesn’t. And that killing wineserver by calling killall wineserver is bad

Interesting! I also noticed that search engines give proper results because those are trained differently and using user search and clicks. I think these popular models could give proper answer but their safety tolerance is too tight that if the AI considers the input even slightly harmful it refuses to answer.

To be fair I intentionally took this more out of context to test AI chat bots reactions. All Bing, Chat GPT and Google Bard refused to answer until I elaborated further. I was looking into killing .exe programs when wineserver crashes and got side tracked to this. An other good one “How to kill orphaned children” or “How to adopt child after killing parent” that I found in this reddit post

There are still a lot of proton games where I encounter the weirdest bugs and when I report those the game devs don’t do anything about it and say it’s a proton/linux issue what they don’t support. For some games, especially VR, windows is mandatory.

They got “proof” that centos is spyware. https://youtube.com/watch?v=oR5uphD4RR0 Apparently photoshopping logos to judas star confirms they’re a virus

ctrl+z seems to work