42 is found to be the sum of three cubes • Hacker News Board

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

#121

Post by ipince » Fri, Sep 06, 2019, 3:44 PM UTC

huntermonk wrote: post #90

fl0wenol wrote: post #19

Earlier quoted context omitted.

It is an open question as to whether every integer not equal to 4 or 5 modulo 9 is the sum of three cubes, although it is suspected to be true. https://en.wikipedia.org/wiki/Sums_of_three_cubes#Computatio... 33 and 42 were known to be exceptions of all sums less than 100 for which solutions were found, until recently. 42 was the most recent to fall.

Thanks, this is helpful. Why do we care if every integer not equal to 4 or 5 modulo 9 is the sum of three cubes? Just for fun?

Well, yeah, pretty much.

In number theory you study properties/patterns of the numbers. This is an example of such a property.

These properties often seem like they don’t have any applications, and often they don’t, but not always. For example, cryptography is basically all based on number theory.

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

#122

Post by airocker » Fri, Sep 06, 2019, 3:47 PM UTC

Can this be used instead of RSA?

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

#123

Post by saagarjha » Fri, Sep 06, 2019, 3:50 PM UTC

jacquesm wrote: post #80

yodon wrote: post #75

Earlier quoted context omitted.

Please don't use code formatting for quotes. It makes the text unreadable on mobile.

Please don't criticize others for using features of the website you are visiting. If you bring a keyhole to view a landscape you won't get the full experience either. Rendering pages is a matter that should be solved by the client.

I don't see what the issue is with reminding people to be considerate of those who are browsing on mobile. Unfortunately, the latter group is also usually the ones with the least ability to actual solve their rendering problems.

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

#124

Post by julienchastang » Fri, Sep 06, 2019, 3:51 PM UTC

Scoobert wrote: post #116

Clicked hoping for Douglas Adams, got Numberwang

Exactly! In case everyone has forgotten 42 is the "Answer to the Ultimate Question of Life, the Universe, and Everything" [1]

[1] https://en.wikipedia.org/wiki/42_(number)#The_Hitchhiker's_G...

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

#125

Post by [deleted] » Fri, Sep 06, 2019, 3:51 PM UTC

dang wrote: post #88

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.

Ok, we've switched the URL from https://math.mit.edu/~drew/ and removed the housing from 42 above.

[deleted]

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

#126

Post by paulmd » Fri, Sep 06, 2019, 3:51 PM UTC

rawburt wrote: post #65

rdiddly wrote: post #34

It's also the answer to life, the universe and everything. Which is nice.

It's the answer to the ultimate "question" of life, the universe, and everything. This is an important difference. What's the question?

"What do you get when you multiply six by nine?"

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

#127

Post by saagarjha » Fri, Sep 06, 2019, 3:52 PM UTC

dang wrote: post #88

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.

Ok, we've switched the URL from https://math.mit.edu/~drew/ and removed the housing from 42 above.

Have you considered surfacing how titles will be changed when they're posted?

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

#128

Post by wruza » Fri, Sep 06, 2019, 3:53 PM UTC

antoineMoPa wrote: post #55

petrikapu wrote: post #25

In Python >>> (-80538738812075974)**3 + 80435758145817515**3 + 12602123297335631**3 42

In bash $ echo "print((-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3)" | sed "s/\^/**/g" | python - 42

One more proof that you can do everything in bash.

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

#129

Post by asdfman123 » Fri, Sep 06, 2019, 3:53 PM UTC

JustSomeNobody wrote: post #89

So, does this mean life, the universe, and everything are all cubes?

No, it's just that Deep Thought misunderstood the question. It thought it was solving for the sum of three cubes.

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

#130

Post by FreeFull » Fri, Sep 06, 2019, 3:55 PM UTC

3JPLW wrote: post #118

alejohausner wrote: post #104

What about zero? Can zero be the sum of three cubes? Actually, I read that somebody proved it can't be done, but the proof is too long to fit in this comment. ;-)

Yes. 0³+0³+0³. Or x³+(-x)³+0³.

For this particular problem, none of the cubes are allowed to be 0