(8,866,128,975,287,528)3 + (–8,778,405,442,862,239)3 + (–2,736,111,468,807,040)3 = 33.
“So what?” you ask: And here’s why:
One reason to find the answers to these so-called “stubborn numbers” is because mathematicians don’t really like having unsolved equations laying around. Another is that finding solutions like this can play a role in some future attempts to find proofs for k = x3+ y3+ z3 or proofs that use it.
What made 33 “stubborn”? The luck of the draw, mostly. It is now known that if you divide an integer by 9 and get a remainder of 4 of 5, that integer cannot be expressed as the sum of three cubes. Excluding those poor unfortunates, the next-to-last integer to be verified was 33, with the complicated-looking equation up top being the actual solution. It took three weeks of supercomputer cycles to find this solution, which suddenly makes bitcoin mining seem almost whimsically simple.
Anyway, 1 through 99 are almost now accounted for. The last holdout: 42, because of course it is.