A Conversation for Fermat Numbers

'avin' a moan

Post 1


First things first, I like this entry, nice and neat. It's good the way it introduces the conjecture that every Fermat number is prime before telling us it's wrong. Of course, I already knew that.

However, I have to point out that none of the four skins renders "22n" as we want. Instead it looks like 2^(2n). I don't know what can be done, but it's misleading as it is.

Also, Polya's result isn't thatinteresting given that Euclid knew there were infinitely many primes. With a simpler proof too. Didn't Polya actually show there are infinitely many Fermat primes? Or was that someone else?

'avin' a moan

Post 2

Gnomon - time to move on

Hi Bagpuss. Sorry the superscript on the superscript didn't work for you. It looks OK on my browser.

I think Polya's proof is interesting. Of course Euclid had already proved it, but Polya's one is neat even if a little long winded, and it doesn't use 'proof by contradiction'. Some people are not 100% happy with that method of proof.

'avin' a moan

Post 3


Well I'm in Internet Explorer here. Mozilla handles it fine. Sorry, I don't understand computers so it didn't occur to me that it could be the browser.

I guess you're right about Polya. There's an easier way without using contradiction, though. You can prove that any natural number has a prime larger than it by basically Euclid's argument, but without reductio ad absurdam.

You know, it'd be good if some of the undergrads here read this article. It's a good demonstration of why proof by example, even several examples, is wrong.

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