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As a result of the revolutionary solution 'Sum-Of-Three-Cubes & # 39; for number 33, a team led by the University of Bristol and the Massachusetts Institute of Technology (MIT) has solved the last element of the famous 65-year old math puzzle project with an answer for the most elusive number of all – 42.
The initial problem, defined in 1954 at the University of Cambridge, sought solutions of the Diophantine equation x ^ 3 + y ^ 3 + z ^ 3 = k, where k represents all numbers from one to 100.
Beyond the small, easy-to-find solutions, the problem quickly became insoluble because the most interesting answers – if they did exist – could not be calculated, as the numbers required were vast.
But slowly, for many years, every value of k has finally been solved for (or has proved insoluble), thanks to sophisticated techniques and modern computers – except for the last two, the most difficult ones; 33 and 42.
Fast forward to 2019 and the mathematical ingenuity of Professor Andrew Booker over weeks on a university supercomputer finally found an answer to 33, which means the last issue in suspense in this old puzzle of several decades, the most difficult to cook, was this favorite Douglas Adams fans everywhere.
However, solving 42 was another level of complexity. Professor Booker turned to MIT mathematics professor Andrew Sutherland, who broke the world record with massively parallel calculations. answer 42 in Hitchhiker's Guide to the galaxy.
The solution of Professors Booker and Sutherland for 42 would be found using Charity Engine; a "global computer" that harnesses the unused and unused computing power of more than 500,000 home computers to create a multi-user ultra-green platform that consists entirely of otherwise lost capabilities.
The answer, which took more than a million hours of calculation to prove, is as follows:
X = -80538738812075974 Y = 80435758145817515 Z = 12602123297335631
And with these almost infinitely improbable numbers, the famous Solutions of the Diophantine Equation (1954) can finally be dropped for any value of k between 1 and 100, even 42.
Professor Booker, based at the School of Mathematics at the University of Bristol, said: "I feel relieved.In this game it is impossible to be certain to find anything. It's like trying to predict earthquakes – there are only rough probabilities.
"So, we could find what we are looking for in a few months, or the solution may not be found for a century."
Source of the story:
Material provided by University of Bristol. Note: Content can be changed for style and length.
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