Erdős Problem #308 — Gaps among integers represented by bounded unit fractions

About 46 years old · traced to 1980

For $N≥1$ , let $S_N$ be the set of integers representable as sums of distinct unit fractions with denominators at most $N$ . What is the least positive integer outside $S_N$ ? Is $S_N$ always an initial interval of the positive integers?

References

Primary source

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique 28 (1980).

Additional references

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique 28 (1980).

number-theory unit-fractions

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