Ridiculous math problems (Quora)

(…) You may have seen such meme images before. They are always pure click-bait garbage: “95% of MIT graduates couldn’t solve this!”, where “this” is some inane, or ill-defined, or trivial brain teaser.

This one is not. The meme is a clever, or wicked, joke. Roughly 99.999995% of the people don’t stand a chance at solving it, and that includes a good number of mathematicians at leading universities who just don’t happen to be number theorists. It is solvable, yes, but it's really, genuinely hard. (…)

You may think that, if all else fails, we can just throw computers at the problem. It’s really easy to write a computer program that searches for solutions of this simple-looking equation. Surely a computer will find them eventually, if they do exist. Wrong. A brute-force search with a computer is totally useless here. (…)

from https://www.quora.com/How-do-you-find-the-positive-integer-solutions-to-frac-x-y+z-+-frac-y-z+x-+-frac-z-x+y-4

Further reading

https://ami.uni-eszterhazy.hu/uploads/papers/finalpdf/AMI_43_from29to41.pdf
https://news.ycombinator.com/item?id=23739243
https://www.dam.brown.edu/people/mumford/blog/2020/Ridiculous.html