/mg/ = /math/ general: Genius Edition

Very elegant, I like it.

That's because I did it by noticing this instead of expanding like a caveman, also I'm not

Meh, knowing an identity like that just takes the fun out of the problem but I guess it works.

Anyways, if anyone cares the problems are all from

fmf.uni-lj.si/~lavric/Santos - Number Theory for Mathematical Contests.pdf

I found this book months ago when I was given a homework problem in number theory and I couldn't do it, I panicked and then I started googling for the problem. It was nowhere to be found so I then went on stackexchange. There the problem had not been asked either, so then I googled for all the number theory problem compilations I could find online and I went looked problem by problem.

I never found the problem like this... but I did find a lot of good problem compilations like this, and I particularly like this one as it adds not only problems but a short list of theorems I can quickly refer to, so I don't need to look elsewhere for theorems and lemmas. And now I'm on vacation so I decided I will do all the problems in the book in the 3 weeks I have free from university.

>instead of expanding like a caveman

Why is /mg/ so mean? I am not a caveman. I just haven't memorized all the algebra identities :(. And I think my proof is better as it is more creative. It is trivial to apply a known identity, but it is non-trivial to square the entire thing and start seeing where that takes you.

You don't need to memorise that. All you need to 'memorise' is that [math] (a \pm b)^2 = a^2 \pm 2ab + b^2 [/math] and [math] (\sqrt{a})^2 = a [/math].

>why are you pointing out i'm retarded?
>i'm just retarded!
You need to fuck off and come back when you have a basic understanding of mathematics.

>Why is /mg/ so mean?
Okay that wasn't very nice, granted.

> It is trivial to apply a known identity
Yes, but it is non trivial to recognize known identities (here (a+b)^2 = ...) in non-obvious situations. That's why integration problems are troublesome (everyone knows fubini, u-sub and integration by parts, but it's another thing to know when and how to do these things).
That being said, in any other situation, I would have done what you did, because it's the natural thing to do.

How do I acquire that basic understanding of mathematics? :c I wanna be like you guys.

Stop ganging up on the guy he made a minor oversight. It happens to everyone sometimes. (R-right?)

Natsuki is the only decent girl in the whole series, and she probably smells like a stinky NEET!