Let be given positive integer and let be the largest integer, such that cannot be written as a sum of unit fractions, that is is not solvable in positive integers . If all is well, is finite for every , although even showing that for , the first non-trivial case, would essentially solve a 60-year old conjecture!

1) Give a superlineair bound on

2) Give a bound on that grows asymptotically faster than

Beeteedubs, if you don’t mind, please don’t solve E-S, or at least share your thoughts. I wanna be a part of it like really really badly 🙂

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