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Results tagged with additive-combinatorics
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user 38851
Questions on the subject additive combinatorics, also known as arithmetic combinatorics, such as questions on: additive bases, sum sets, inverse sum set theorems, sets with small doubling, Sidon sets, Szemerédi's theorem and its ramifications, Gowers uniformity norms, etc. Often combined with the top-level tags nt.number-theory or co.combinatorics. Some additional tags are available for further specialization, including the tags sumsets and sidon-sets.
2
votes
1
answer
80
views
Chain of sequences, such that $a_{k+1}(n)$ completes $a_k(n)$
We say that the sequence $a_{k+1}(n)$ is a complete sequence of $a_k(n)$ if:
(1) Every term of $a_k(n)$ can be written as a sum of distinct terms of $a_{k+1}(n)$.
(2) $\lim_{n\to\infty} \frac{a_k(n)}{ …
- 3,866
8
votes
Density of all n such that 2^n-1 is square free
To my best knowledge, we don't know even if the set $S$ has an infinity of elements.
In other words we don't know if there exist infinitely many squarefree numbers of the form $2^n-1$.
So,i think thi …
- 3,866
5
votes
0
answers
239
views
The sum of all the elements of every non empty subset of $A$ is not a multiple of $n$
Let $N=\{1,2,\ldots ,n\},n>1$. We wish to construct a set $A\subseteq N$ with the property:
The sum of all the elements of every non empty subset of $A$ is not a
multiple of $n$.
Question: W …
- 3,866
11
votes
1
answer
494
views
Which of these sums appear most often?
Let $N=\{1,2,3,\ldots, n\}$.
We sum all the elements of every nonempty subset of $N$.
Which sum(s) appears most often? (Let's call this sum a champion).
Using a simple pigeonhole argument a champion m …
- 3,866
1
vote
0
answers
98
views
Reference request for a result in additive combinatorics
Let $p$ be a prime number and $[p-1]=\{1, 2, \ldots, p-1\}$.
The following proposition is proved: (but I cannot find out where)
Proposition: The non-empty subset sums of $[p-1]$ are equally distribut …
- 3,866
21
votes
1
answer
770
views
Avoiding multiples of $p$
Let $p$ be a prime number and $P=\{1,2,...,p-1\}$
In how many ways we can sum all the elements of $P$ in such a way that we will reach a multiple of $p$
only when we sum the last summand?
For …
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