If integers are chosen from integers , show that, among the chosen integers, there are two, such that one of them divides the other.
I cant remember exactly how to do this but what you have to note is that any integer can be written in the form where and a is odd. Note also that in this case a has n values since there is n odd and n even integers between 1 and 2n.
Now you have to use the pigeonhole principle. How exactly i cant remember. But im guessing since there n values of a and you choose n+1 integers you'll end up at the fact that one 'hole' has 2 'pigeons' in it.