Solving a HARD Number Theory problem from the USA Math Olympiad Program

Gear Up! We are going to solve a hard number theory problem from the 2004 USA Math Olympiad Program and... Don't just guess the solutions! Prove it! Let's see if you are capable of making into the math camp! Make sure to watch all of the video or else these triples (x, y, z) will come and find you at night.
Typo at 0:23: A "+" is missing.
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[@1psi3colourmath]

A Nice Number Theory Practice:
czcams.com/video/KufAgolhrR4/video.html

[@shadow_1213]

I proved the problem...
It satisfy for all perfect Pythagorean triangle belonging XY plane with polar radio less than or equal to sphere radius 2^2004 (and for all integer sphere radius).

[@shadow_1213]

Not possible find other more solutions than ±2^1002 because:
If imagine constructing sphere below generally Pythagorean Form of the sphere equation, the values of x & y must be represented by rcos(Θ) and rsen(Θ), respectively (polar representation of x & y).
So, the values for {0,π/2,π, 2π/3,2π} satisfy the equation, but in 0

[@NghixaTwf]

wait i also like maths, play geometry dash, minecraft and chess same as you ? this is very coincident :)

[@goldensaddle1361]

You just solved a math Olympiad question in a yt comment section like it's nothing 💀💀
Howw ? I always try to be better at math but I suck

[@shadow_1213]

Hehe 😅 I play chess sometimes 😁

[@shadow_1213]

HASHAHS well, simple logic.
In math not just exist 1 way to get a solution to a problem 😅

[@NghixaTwf]

@@goldensaddle1361 tbh the solution shown in the video is not that hard to think of. but this guy's solution is insane

[@BENP781]

Zez