/sci/ - Science & Math

It's been almost 10 years since the meme haruhi superpermutation stuff. I say it's time we do some progress on another obscure combinatorics problem.

>>11825475
>>11825497
>What you want is called a "primitive root modulo n", and finding an algorithm to generate one for arbitrary n that doesn't suck shit is still an open problem.
that's not true, though
first of all, there is a generator for Z/nZ iff n=2, n=4, or n=p^k or n=2p^k for some odd prime p
secondly, there are [math]\phi(n)[/math] generators, out of all the n residues
literally "pick a random residue and check if it's a primitive root" is a good algorithm, because you have roughly a [math]\frac{p-1}{p}[/math] chance of choosing a primitive root

Let [math]X = \{ 1/2^n : n \geq 1\}[/math].
Let's also use the standard notation [math]aX + b = \{a/2^n + b : n \geq 1\}[/math].
Does there exist a set [math]S \subseteq \mathbb{R}[/math] of positive Lebesgue measure, such that [math]aX+b[/math] is not a subset of [math]S[/math] for all [math]a, b \in \mathbb{R}, a \neq 0[/math]?
Look up "erdos similarity problem" if you care, but no one knows the answer. SAD!

>>11707208
to me, the purpose of an imageboard is "you are free to post anonymously" not "you are obliged to post anonymously"

>use 26-base system
>everyone needs to learn 26x26 multiplication tables

let A be a nxn matrix. Each entry is chosen randomly independently to be equal to 1 with probability p, otherwise 0.
What is the expected norm of A?