Let delta(N) be the minimal non-zero value of | 1-∑_n∈ Afrac1n| as A ranges over all subsets of 1,…,N. Is it true that delta(N)=e^-(c+o(1))N for some constant c∈ (0,1)?

Erdős Problem #311 — Let $\delta(N)$ be the minimal non-zero value of $\lvert 1-\sum_{n\in A}\frac{1}{n}\rvert$ as $A$ ranges over all subsets of $\{1,\ldots,N\}$ .

About 46 years old · traced to 1980

Let $\delta(N)$ be the minimal non-zero value of $\lvert 1-\sum_{n\in A}\frac{1}{n}\rvert$ as $A$ ranges over all subsets of $\{1,\ldots,N\}$ . Is it true that $\delta(N)=e^{-(c+o(1))N}$ for some constant $c\in (0,1)$ ?

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.

number-theory unit-fractions

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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