Let A⊂ N be an additive basis of order 2. Must there exist B=b_1<b_2<…⊆ A which is also a basis such that lim_k→ ∞fracb_kk^2 does not exist?

Erdős Problem #326 — Let $A\subset \mathbb{N}$ be an additive basis of order $2$ . Must there exist $B=\{b_1<b_2<\cdots\}\subseteq A$ which is also a basis such that $\lim_{k\to \infty}\frac{b_k}{k^2}$ does not exist?

At least 45 years old · documented by 1980

Let $A\subset \mathbb{N}$ be an additive basis of order $2$ . Must there exist $B=\{b_1<b_2<\cdots\}\subseteq A$ which is also a basis such that $\lim_{k\to \infty}\frac{b_k}{k^2}$ does not exist?

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-basis number-theory

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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