Mathematicians find elusive number in 'sum-of-three-cubes' puzzle

Over the course of many years, each value of k was eventually solved.
The last outstanding number was 42 after Andrew Booker of the University of Bristol earlier this year found the answer to the penultimate missing number, 33, by devising an algorithm and using weeks of processing time on a university supercomputer.
To achieve the solution for 42, Booker worked with Andrew Sutherland of the Massachusetts Institute of Technology (MIT) in the US using Charity Engine, which deploys unused computing power from over 500,000 home PCs.
A million hours of processing later, they came up with the answer:
42 = (-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3
"I feel relieved. In this game it's impossible to be sure that you'll find something. It's a bit like trying to predict earthquakes, in that we have only rough probabilities to go by," Booker said in a statement.
By "cosmic coincidence" both the number 42 and the extensive use of computers featured in Douglas Adams' cult science fiction novel "The Hitchhiker's Guide to the Galaxy," the statement noted.
Sutherland is known for using massively parallel computations, at times likened to "Deep Thought," the giant machine which gives the answer 42 in Adams' novel.
"When I heard the news, it was definitely a fist-pump moment," Sutherland said.
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