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Life, the Universe, and Math: 42 Proven to be the Sum of 3 Cubes

posted by Fnord666 on Friday September 13 2019, @08:26PM   
from the for-all-values-of-everything<113 dept.

MrPlow writes:

Submitted via IRC for chopchop1

The problem of 42 — at least as it relates to whether the number could be considered the sum of three cubes — has finally been solved. The question of whether every number under 100 could be expressed in this fashion has been a long-standing puzzle in the world of mathematics. Now, two mathematicians, Andrew Sutherland of MIT and Andrew Booker of Bristol, have jointly proven that 42 is indeed the sum of three cubes.

*SPOILER* (click to show) *SPOILER* (click to hide)

In the equation x³+y³+z³ = k, let x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. Plug it all in, and you get (-80538738812075974)³ + 80435758145817515³ + 12602123297335631³ = 42.

Source: https://www.extremetech.com/computing/298112-life-the-universe-and-math-42-proven-to-be-the-sum-of-3-cubes

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Original Submission

• Read and learn, and it's not a joke Read and learn, and it's not a joke (Score: 3, Informative) by janrinok on Saturday September 14 2019, @11:02AM (2 children)

  by janrinok (52) on Saturday September 14 2019, @11:02AM (#894025) Journal

  I guess you didn't read TFS then....

  For years, mathematicians have worked to demonstrate that x3+y3+z3 = k, where k is defined as the numbers from 1-100. By 2016, researchers had demonstrated that this theory held true in all cases except for two unproven exceptions: 33 and 42. The formal theory, as expressed by Roger Heath-Brown in 1992, is that every k unequal to 4 or 5 modulo 9 has infinitely many representations as the sum of three cubes. By closing this particular gap, we’ve now proven that all numbers below 113 fit this theory.

  So, this isn't a joke. The numbers 33 and 42 have been causing a problem for quite some time. Another comment said that the answers could be easily brute forced - but for some reason they weren't. So perhaps this wasn't as simple to solve as many seem to thing it was.

  Parent

  Starting Score:	1		point
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• Re:Read and learn, and it's not a joke (Score: 2) by janrinok on Saturday September 14 2019, @11:04AM

  by janrinok (52) on Saturday September 14 2019, @11:04AM (#894026) Journal

  s/thing/think/

  Parent

• Re:Read and learn, and it's not a joke (Score: 0) by Anonymous Coward on Tuesday September 17 2019, @01:25PM

  by Anonymous Coward on Tuesday September 17 2019, @01:25PM (#895126)

  These are very informative. View in order (or just jump to the third for the punchline): 1 [youtube.com], 2 [youtube.com], and 3 [youtube.com].

  Parent