The problem below was posted in around 2018 as a mischievous internet meme, '95% of people cannot solve this!'.
Can you find positive whole numbers for a, b, and c?
I missed it at the time and I'm only just catching up. 95% is a bit of an underestimate.
If you'd played around with it a bit and maybe written some code to search you probably wouldn't have got very far, because the numbers in the smallest solution are about 80 digits long! [1]
Python can check the solution for us without blinking.
>>> a = 154476802108746166441951315019919837485664325669565431700026634898253202035277999
>>> b = 36875131794129999827197811565225474825492979968971970996283137471637224634055579
>>> c = 4373612677928697257861252602371390152816537558161613618621437993378423467772036
>>> a/(b+c) + b/(c+a) + c/(a+b)
4.0
But this is nothing! If we change the 4 to 37298 the smallest solution has numbers of 194,911,150 digits [1], which I won't display for obvious reasons.
If we go for 896 we then get trillions of digits, like about 1000,000,000,000+ digits. For those who like statistics, if we printed out three such numbers in 12 point type, on double sided A4 paper, the paper would fill, wait for it... yes, an Olympic Swimming Pool.
For an accessible explanation, not too technical, of how to solve the original question from scratch, with some help from Python, see [2].
For a fuller article that going into a bit more theory, but is very good, see [3].
[1] https://observablehq.com/@robinhouston/a-remarkable-diophantine-equation