Erdős Problem #305 — Largest denominator needed for a rational Egyptian fraction

About 46 years old · traced to 1980

For integers $1≤a<b$ , let $D(a,b)$ be the least possible largest denominator in a representation of $a/b$ as a sum of distinct unit fractions, and let $D(b)=\max_{1≤a<b}D(a,b)$ . Is $D(b)≤b(\log b)^{1+o(1)}$ as $b→∞$ ?

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

InErdős Problems

Posted 1 month ago

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

No solutions have been posted yet.