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Results tagged with additive-combinatorics
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user 2480
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.
10
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0
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Is almost every number the sum of two numbers with small radicals?
Define a set of numbers with small radicals (A341645 in OEIS) by
$$A_2=\{n\in\mathbb{N} \;|\; \text{rad}(n)^2\le n\}$$
The asymptotic density of $A_2\cap \{1,\dots N\}$ is $\sqrt{N}\times e^{2(1+o(1)) …
- 5,103
9
votes
Positive integers written as $\binom{w}2+\binom{x}4+\binom{y}6+\binom{z}8$ with $w,x,y,z\in\...
Not an answer - but I decided to delete a prior comment and repost as an answer, because I think it puts the 2-4-6-8 conjecture in a different light than considered so far, hopefully leading to some o …
- 5,103
3
votes
1
answer
250
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Are there unique additive decompositions of the reals?
Given $b\in \mathbb{R}_{>1}$ is there $U\subseteq\mathbb{R}_{\ge 0}$ such that $U+bU=\mathbb{R}_{\ge 0}$ and $(U-U)\cap b(U-U)=\{0\}$ (or equivalently: $u+bv=u'+bv' \implies u=u', v=v'$)?
Here is an …
- 5,103
0
votes
Is the set $ AA+A $ always at least as large as $ A+A $?
I think $\big\{-1, 0, \frac{1+\sqrt{5}}{2}\big\}$ is a counterexample.
THIS IS WRONG, see comments, but I'll leave it up as a warning.
- 5,103