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Let $p$ be a prime. For finite field $\mathbb{F}_{p^k}$ and $d\in\mathbb{Z}^+$, I am considering the following quantity, where we interpret the field $\mathbb{F}_{p^k}$ also as a $\mathbb{F}_p$-vector ...

Definitions: let $n \in \mathbb{N}_{>0} \cup \{ \infty \}$ and let $E_n$ be the set of sequences $(d_i)_{i=1}^n$ such that $d_1=1$, $d_i$ is an even integer (for $i > 1$) and $0<d_i \le i$. ...

I was working on a problem that consisted of deciding if the language a finite automaton (the alphabet of which is $\{0,1\}$ and the words accepted are binary encoded positive integers) contains an ...

Erdos defined $f(n)$ to be the minimum $r$ such that there is an $r$-coloring of the positive integers less than $n$, wherein $n$ cannot be written as the sum of distinct monochromatic integers. ...