Off Topic - MegaFavNumbers - My Favorite Large Numbers
101#MegaFavNumbers
Whilst this channel is about the online game Path of Exile, from time to time (at most one per month) I do off topic videos - this is one of those. Channel regulars will know I have a maths background and can't shut up about statistics.
Well, a number of educational and mathematics related channels have created a challenge to make videos about 'your favorite number over one million'.
I thought I'd jump on that bandwagon, and I've picked a set of three related numbers.
These three numbers are the smallest solutions to the (absolutely sadistically difficult) problem with the fruits in the thumbnail. I got completely nerdsniped by this problem, which looks relatively accessible, but there's probably only a few thousand people worldwide who could solve it. Even though I wrote a thesis strongly related to the main topic required to solve this (the group of rational points on an elliptic curve), there is a step I don't understand in the solution.
154476802108746166441951315019919837485664325669565431700026634898253202035277999, 36875131794129999827197811565225474825492979968971970996283137471637224634055579, 4373612677928697257861252602371390152816537558161613618621437993378423467772036
Alon Amit's full solution to the problem on Quora:
https://www.quora.com/How-do-you-find-the-positive-integer-solutions-to-frac-x-y%2Bz-%2B-frac-y-z%2Bx-%2B-frac-z-x%2By-4/answer/Alon-Amit
This is a difficult proof to follow, so I only sketch it in the video. The key concepts require an understanding of group theory, usually taught in second or third year undergraduate pure maths courses.