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42 is found to be the sum of three cubes

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Re: 42 is found to be the sum of three cubes

#101

Post by xhroot »

taneliv wrote: post #78
zests wrote: post #63

Earlier quoted context omitted.

In dc/shell/bash dc -e '_80538738812075974 3 ^ 80435758145817515 3 ^ 12602123297335631 3 ^ + + p'

In SQL: SELECT (-80538738812075974::NUMERIC)^3 + 80435758145817515::NUMERIC^3 + 12602123297335631::NUMERIC^3;

Javascript in FF/Chrome:

    > (-80538738812075974n)**3n + 80435758145817515n**3n + 12602123297335631n**3n
    42n
https://caniuse.com/#search=bigint

Re: 42 is found to be the sum of three cubes

#103

Post by jjtheblunt »

isotropy wrote: post #21

For context, 42 was the only remaining number below 100 where it wasn’t known if this was possible. The general problem of exactly which numbers are the sum of three cubes is unsolved. https://en.m.wikipedia.org/wiki/Sums_of_three_cubes

Isn't the set of all triples of integers be enumerable, because (inductively) the set of all pairs of integers is enumerable (thanks, Cantor)?

Then, if one could enumerate all triples of integers, one could, for each triple, calculate the sum of the cubes.

So, integers which are sums of cubes are enumerable. That doesn't mean they're a known recursive set, just recursively enumerable.

Am I missing something? Perhaps the statement "The general problem of exactly which numbers are the sum of three cubes is unsolved." is meant to imply "not known to be a recursive set", i.e., no known algorithm for finite time answering the question of whether a given integer is in the set?

Re: 42 is found to be the sum of three cubes

#105

Post by gerdesj »

techolic wrote: post #2

See also https://twitter.com/robinhouston/status/1169877007045296128 . I was prompted the twitter link has been submitted but wasn't able to find it. Edit: And apologies for using unicode ㊷ in the title, the ascii 42 was removed from the title after initial submission.

I've just installed ttf-code2000 just so I could see that character in your comment!

Re: 42 is found to be the sum of three cubes

#106

Post by ArneVogel »

JshWright wrote: post #7
thekyle wrote: post #5

Could someone elaborate on why this is interesting? The linked page doesn't have much context.

Numberphile is a great resource for pretty much any "pop math" topic. https://www.youtube.com/watch?v=ASoz_NuIvP0

They also just released a video on 42: https://www.youtube.com/watch?v=zyG8Vlw5aAw

Re: 42 is found to be the sum of three cubes

#110

Post by theothermkn »

mombul wrote: post #27

Yeah but now, what? What was learned from this? Why did we look for a solution in the first place? How is it important that a number can be a sum of three cubes?

Just googling "42 sum of 3 cubes" would have yielded better answers with less fuss. In general, I always google before asking in a forum. It's like not littering.

https://www.google.com/search?client=ubuntu&channel=fs&q=42+...

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