"I experimented with the tasks of the cubic representation in the style of the previous work of Andrew and Richard Guy. The numerical results were amazing ... "( comment on MathOverflow)That's how the retired mathematician Allan MacLeod came across this equation several years ago. And it's really very interesting. Honestly, this is one of the best Diophantine equations I've ever seen, but I did not see very many of them.
I found it when it began to spread like a network-nesting picture-pseudomem, invented by someone's ruthless mind ( Sridhar , was it you?). I did not understand right away what it is. The picture looked like this:
"95% of people will not solve this riddle. Can you find positive integer values? "
You probably already saw similar pictures-memes. It's always the cleanest rubbish, clickbites: "95% of MIT graduates will not decide it!". "She" is some stupid or poorly formulated task, or a trivial warm-up for the brain.
But this picture is completely different . This meme is a clever or malicious joke. Approximately 99.999995% of people have not the slightest chance to solve it, including a good part of mathematicians from leading universities that do not deal with the theory of numbers. Yes, it is solvable, but at the same time it is really complicated. (Incidentally, it was not invented by Sridhar, more precisely, not completely.) See the story in this comment ).
You might think that if nothing else helps, then you can just make the computer solve it. It is very simple to write a computer program to find solutions to this seemingly simple equation. Of course, the computer will find them sooner or later, if they exist. Big mistake . Here the method of simple computer enumeration will be useless.