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September 8th, 2019, 11:37
Interesting observation, Alrik.

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September 8th, 2019, 13:05
The header of the 42 video ("42 was the last remaining number below 100 which could not be expressed as the sum of three cubes") is a bit misleading, as there are numbers (for instance 4, 5, 13 and 14) that cannot be expressed this way (evident from the video, goto 0:56). The correct is that "42 was the last possible integer below 100 to be expressed as a sum of three cubes" (Wikipedia). In other words, the last number <100 for which we didn't know if there was a solution. Now we do.

The problem with 4,5… is descibed explicitely in an older video, from before the solution to 33 was found: "The Uncracked Problem with 33 - Numberphile" (https://www.youtube.com/watch?v=wymmCdLdPvM).

pibbur who wonders if his height (191) can be expressed as a sum of 3 cubes, but observes that it's (regrettably?) regarded as an odious number. Whatever that is.
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September 8th, 2019, 13:29
191 has some solutions - these two are nice:

191= 7^3 - 5^3 - 3^3
191= 7^3 - 6^3 + 4^3

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September 8th, 2019, 15:40
Isn't that the same as saying (-5^3-3^3) == (-6^3 + 4^3); which means that any prefix can be used to reach the same results (i.e, 8^4 - …. == 8^4 …. ) =3944 ?

Originally Posted by HiddenX View Post
191 has some solutions - these two are nice:

191= 7^3 - 5^3 - 3^3
191= 7^3 - 6^3 + 4^3

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September 8th, 2019, 16:13
yeah, you can always easily generate two solutions
beginning with 6:

6^3 - 5^3 - 3^3 = 64
6^3 - 6^3 + 4^3 = 64

7^3 - 5^3 - 3^3=191
7^3 - 6^3 + 4^3=191

8^3 - 5^3 - 3^3=360
8^3 - 6^3 + 4^3=360

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September 12th, 2019, 05:59
In case you hadn't seen this:
https://www.sciencealert.com/the-sum…48u-c84umxBUIY
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September 12th, 2019, 10:00
Originally Posted by Hurls View Post
In case you hadn't seen this:
https://www.sciencealert.com/the-sum…48u-c84umxBUIY
"The pair had to go large, so they enlisted the aid of the Charity Engine, an initiative that spans the globe, harnessing unused computing power from over 500,000 home PCs to act as a sort of "planetary supercomputer".

It took over a million hours of computing time…
"

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