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I remember reading a proof to the fundamental theorem of arithmetic (every number is composed of a unique multiple of primes) in a number theory book and really
by trengrj 10y ago
I remember reading a proof to the fundamental theorem of arithmetic (every number is composed of a unique multiple of primes) in a number theory book and really enjoying it. I would disagree with Gowers and say it is obvious intuitively, but I'd still argue it is worth writing a proof for.
- Smaug123 10y agoIt really isn't obvious (I promise!), and Gowers's Answer 4 is "the real reason" for a mathematician. Alternatively viewed, it is not obvious that Euclidean domains are unique factorisation domains. (Though it is obvious that EDs are principal ideal domains, so the alternative view becomes "it is not obvious that PIDs are UFDs".)
- TopologyDough 10y agoThe link misinterprets FTA.
- rahimnathwani 10y agoAlthough it was ~30 years ago, I recall doing some school homework when we had just learned about prime numbers and factorisation. I remember trying to divide by random primes until I came across a factorisation. It wasn't at all obvious to me (at ~10 years old) that prime factorisations were unique or that they could be found using a simple repetitive algorithm. It seems obvious now, but only because I've never come across an integer with more than one factorisation. If there were an article on HN tomorrow with the headline 'Integer with more than one prime factorisation found' I wouldn't be able to resist clicking the link.
- AimHere 10y ago> If there were an article on HN tomorrow with the headline 'Integer with more than one prime factorisation found' I wouldn't be able to resist clicking the link. Curiously, I've only just found out that 48016416432886585186892071037001629018831524915070361 17449649760043615376581136847123881454516238486352419 62687300988949648670959062041377941995335910356581948 79838588416610716340382432762472099541373300228025778 94213135434471675634979394732216151334015571089605667 2861 has two distinct prime factorizations, thus providing a counterexample to Euclid's Fundamental Theorem of Arithmetic and showing that he made a mistake somewhere. Unfortunately the truly marvellous lists of factors are too small to fit in a Hacker News comment, so you'll have to rediscover the details yourself.
- vinchuco 10y agoYour comment has destroyed the browsing experience on mobile :)
- AimHere 10y agoHah. Apologies for that! I thought the downvotes were because it was a lame joke, not that I was destroying the site!
- umanwizard 10y agoFWIW, I downvoted you because it's a lame joke.
- wlesieutre 10y agoAlso on desktop. Can we get some max-width and overflow:scroll in here?
- ColinWright 10y agoPlease edit this to restore the formatting to something usable. Edit: Thank you.
- CarolineW 10y agoI would rather trust the proof of the Fundamental Theorem of Arithmetic than trust the bald and unsupported assertion by someone I don't know and haven't heard of. Sorry. :-(
- AimHere 10y agoOh, that's fine. I don't want anyone to trust me, I just wanted to get the OP to go to the trouble of checking up on me, since he or she is willing to go at least partways in that direction :)
- clux 10y agoDamn that Fermat margin.