1
vote
1answer
283 views

Valid Difference Sets

Suppose $$ P \subseteq \{1,2,\dots,N\},\quad |P| = K $$ We calculate the differences as: $$ d=p_i-p_j\mod N,\quad i\ne j $$ Now let $a_d$ denote the number of occurrence of $d$ (for $d = 0, 1, 2, ...
4
votes
2answers
380 views

Average involving the Euler phi function

Does $$\frac{1}{N^2}\sum _{d=1}^N \log d \sum _{n=1}^{N/d} \frac{\phi(n)}{\log (dn)},$$ converges or not when $N$ goes to infinity?
3
votes
1answer
358 views

Optimize / simple Set Covering Problem

Let $k,m\in\mathbb{N}$ be given. Let $M:=\{0,... , m-1\}$. How to find a subset $T\subset M$, $|T|=k$ such that $|T+T|$ is maximal, where $T+T=\{ (a+b)\mathbin\%m \mid a\in T,b\in T \}$ (“%” means ...