/sci/ - Science & Math

Might as well listen to some good music while we're waiting for this to start
https://youtu.be/C8CHkd0gX0I

Is there some natural structure that can be built out of the Pythagorean triples? They have some nice properties, e.g. a scalar times a triple is itself a triple. There exists exactly n triples of the form (p^n, b, c) where p is prime, primitive triples remind me, but perhaps only from the name, of primes, etc.

>>11708007
Ironically my study habits improved a lot now that I'm not going to uni.

How do we know that every non-negative real number has an n-th root? I.e. how do we know that there doesn't exist some real number x, such that x^(1/n) isn't real?