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Results tagged with sumsets
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user 38624
7
votes
Sumsets with distinct numbers, upper bound for maximum element
It can be shown that $S(n) \sim n^2$. The upper bound (constructing large Sidon sets) was given in Fedor Petrov's answer, and is a construction of Bose and Chowla. The lower bound (showing that Sido …
- 43.7k
27
votes
Accepted
Distribution of $a^2+\alpha b^2$
There is a positive proportion of such integers and this follows from work on the Berry-Tabor conjecture due to Eskin, Margulis and Mozes (there is work by many others on this; see these papers for re …
- 43.7k
11
votes
Accepted
Size of sets with complete double
Let $S\subset [1,N]$ with $S+S=2N$. I will show that $S$ must have at least $(2.033 +o(1))\sqrt{N}$ elements for large $N$. The argument can certainly be improved, but I don't know what the right a …
- 43.7k