/sci/ - Science & Math

Has anyone any hints on how to achieve higher concentration? In the last years, it seems to me that I've partially lost the ability to focus as much as a I used to, and I want to change that. I'm not talking about medication, but rather some sort of mental exercise or something equivalent. Any ideas?

Since Uni has started again, I decided to brush up my proof skills since I've neglected them before.

I was wondering about something simple, such as proving divisibility:

e.g. <span class="math"> 3 | 2^(2k +1) - 2 [/spoiler]

(inb4 homework thread: This is an example problem, I don't care about the solution, but instead about the approach with which you tackle it).

Is it just induction? I tried and didn't find a proper way to use it.

Hey /sci/,

I've got a combinatorics question, but I have no clue if there's actually a real solution for it, so I thought maybe someone here could help with it.

Assume you have 12 people. These twelve people are supposed to play chess against each other weekly, but only six per meeting, and everyone is supposed to play roughly every second week.

There are 34 weeks (meetings) total. The matchups between the six people at one meeting do not matter.

How do you divide up the players so everyone gets to play as much as everyone else?
Any ideas?

It is correct to write
<span class="math">(a)^n[/spoiler]
instead of
<span class="math">\prod \limits_{m=0}^{n} a[/spoiler],
as long as m=0, right? If not, I might have found the problem that is keeping me from proving an otherwise not-so-hard equation.