# Questions tagged [sidon-sets]

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### On fifth powers forming a Sidon set

We call a set of natural numbers $\mathcal S$ to be a Sidon Set if $a+b=c+d$ for $a,b,c,d\in \mathcal S$ implies $\{a,b\}=\{c,d\}$. In other words, all pairwise sums are distinct. Erdős conjectured ...
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### Primality radii and Sidon sets

I learned tonight what a Sidon set is, in a book about Erdős. This notion inspires me the following question : For $n$ a large enough composite integer, say $r>0$ is a primality radius of $n$ if ...
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### $B_k[1]$ sets with smallest possible $m = \max B_k[1]$ for given $k$ and $n = \lvert B_k[1]\rvert$ elements

Sidon sets are sets $A \subset \mathbb{N}$ such that for all $a_j,b_j \in A$ holds $$a_1+a_2=b_1+b_2 \iff \{a_1,a_2\}=\{b_1,b_2\}.$$ Thus if you know the sum of two elements, you know which elements ...
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### Selecting $k$ integers from an interval $[0, N]$ to maximize the minimum difference between pairwise sums
I have an optimization problem where I need to select $k$ integers over the interval $[0, N]$ s.t. I maximize the minimum difference between any pairwise sum of the $k$ integers (where we also include ...