/sci/ - Science & Math

If you disregard the integer 1, then yes. You can generalize the argument that sqrt(2) is irrational.

whats are "pairs of prime factors"?

If it has any odd powers of prime factors it will be irrational, by pretty much the same proof as for root 2.

Here's an example:

21 = 7 * 3
sqrt(21) = sqrt(7) + sqrt(3)

Since sqrt(7) and sqrt(3) are both irrational, an irrational number plus another irrational number = irrational number

qed

>>5027063
>21 = 7 * 3
>sqrt(21) = sqrt(7) + sqrt(3)

>an irrational number plus another irrational number = irrational number

lulz

>>5027063
Hello, EK

>>5027063
I wish people wouldn't delete their posts so I could see how stupid they are. I mean come on, it's an anonymous website, why be embarrassed?

>>5027084
>not having 4chanx

>>5027084
It's all been archived.

>>5027014
Yes and this is very easy to prove. Let <span class="math">p^{2n+1}m[/spoiler] be any integer such that <span class="math">gcd(p,m) =1[/spoiler]. If the square root of this is rational, say <span class="math">a/b = (p^{2n+1}m)^{1/2}[/spoiler] then you run into a contradiction as follows. Re-write into <span class="math">p^{2n+1}mb^2 = a^2[/spoiler]. Notice that any prime factor of <span class="math">a^2[/spoiler] occurs an even number of times. The left hand side though has an odd number of factors <span class="math">p[/spoiler] (exactly 2n+1 + 2k such factors, where k is however many times p appears in the factorization of b). This is a contradiction to the unique factorization of integers.

Your problem is the special case when n = 0.

>>5027084
http://archive.installgentoo.net/sci/thread/5027063

guys wtf? its totally fine to delete your post if you realise you've made an error
no need to be total dicks and jump all over it.

>>5027109
>>5027109

>>5027109
Then why don't YOU delete all of your posts? Every single one of them is wrong and contains nothing but shitposting of lowest quality.

>>5027116
EK's posts are superb! You're a loser.

>>5027149
Removing your trip in order to samefag, how original.

Cue posts denying any association with your samefag post.

Stupid bitches, what the fuck is going through their pea brains?????

>>5027158
ha! that aint even true, asshat.
i never samefag, but i also never care what you think. so go fuck yourself.

>>5027179
You can't get upset about people insulting your reputation if you have no name to protect.
i.e. Lose the trip--lose the butthurt.