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Results tagged with nt.number-theory
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user 168142
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
6
votes
0
answers
136
views
Maximal coprime-free subsets of $[n]$
I am working on a problem in which it is important to study the maximal coprime-free subsets of $[n] = \{1,2,\ldots,n\}$. (A set $S\subseteq [n]$ is coprime-free if for all
$i,j\in S$ with $i\ne j$, $ …
- 807
2
votes
1
answer
110
views
Counting numerical semigroups by largest element of minimal generating set
For a given integer $n$, I am interested in the number of different numerical semigroups one can make with a generating set consisting only of integers in $[n]$.
I have done some small examples. For $ …
- 807
2
votes
1
answer
396
views
Sets with certain property concerning density of sumsets
I am working with subsets of $[n]$ of the form $(A+B)\cap A$, where $A+B$ is a sumset. Namely, I am interested if there are nonempty sets $B$ such that whenever $A$ covers a positive proportion of $[n …
- 807
9
votes
1
answer
256
views
Arithmetic progressions in inverse image of totient function
I noticed on the OEIS that there are various sequences (e.g. A050515-A050520) that describe arithmetic progressions whose totients are all equal. For example, we have
$$\varphi(\{1,2\}) = 1$$
$$\varph …
- 807
10
votes
2
answers
921
views
Converse to Erdős' conjecture on arithmetic progressions
I apologise in advance if this has been asked here before. I did a search and did not find anything obvious. Erdős' conjecture states that if $A\subseteq {\bf N}$ is such that $\sum_{n\in A} n^{-1}$ d …
- 807