Let f(N) be the size of the largest quasi-Sidon subset A⊂1,…,N, where we say that A is quasi-Sidon if | A+A|=(1+o(1))binom| A|2. How does f(N) grow?

Erdős Problem #840 — Let $f(N)$ be the size of the largest quasi-Sidon subset $A\subset\{1,\ldots,N\}$ , where we say that $A$ is quasi-Sidon if $\lvert A+A\rvert=(1+o(1))\binom{\lvert A\rvert}{2}.$ How does $f(N)$ grow?

About 45 years old · traced to 1981

Let $f(N)$ be the size of the largest quasi-Sidon subset $A\subset\{1,\ldots,N\}$ , where we say that $A$ is quasi-Sidon if $\lvert A+A\rvert=(1+o(1))\binom{\lvert A\rvert}{2}.$ How does $f(N)$ grow?

References

Primary source

ULAM AI, UnsolvedMath dataset, Erdős Problems set, revision b9437975f3c873f635a13c48f8b022f5ba80898a; CC BY 4.0.

Additional references

UnsolvedMath, Erdős Problems set, ULAM AI, licensed CC BY 4.0.

additive-combinatorics sidon-sets

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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