Paul Erdős's notes on Egyptian fractions are with <A HREF="https://en.wikipedia.org/wiki/Ronald_Graham">Ronald Graham,</A> who has reproduced some of them in <A HREF="http://www.math.ucsd.edu/~ronspubs/13_03_Egyptian.pdf">Paul Erdős and Egyptian Fractions.</A> Graham mentions one unfinished manuscript in which "it is shown that any integer can be represented as a sum of reciprocals of distinct numbers which each have exactly three prime factors". This was only published in 2015. As this <A HREF="https://www.simonsfoundation.org/2015/12/10/new-erdos-paper-solves-egyptian-fraction-problem/">commentary</A> aptly notes *"Nearly 20 years after his death, the famed mathematician Paul Erdős keeps on publishing, thanks to the conjectures he left behind and the friends who strive to prove them."*

<IMG SRC="https://ilorentz.org/beenakker/MO/Erdos_1.png"/>

The <A HREF="http://www.math.ucsd.edu/~ronspubs/pre_tres_egyptian.pdf">2015 publication</A> by Butler, Erdős, and Graham ends with this comment: *"One of the authors believes that all rational numbers can be expressed in this form, another author has doubts that every rational number can be expressed in this form, and the third author, already having looked in <A HREF="https://en.wikipedia.org/wiki/Proofs_from_THE_BOOK">The BOOK</A> at the answer, remains silent on this issue."*

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An altogether different "treasure trove" is formed by the letters which Paul Erdős wrote throughout his life. The Archive for American Mathematics has digitised 435 letters from Erdős to Carl Pomerance, accessible <A HREF="https://www.cah.utexas.edu/collections/math_erdos.php">here,</A> and is solliciting further donations of correspondence. A commentary entitled <A HREF="http://digitaleditions.walsworthprintgroup.com/publication/?i=161614#{"issue_id":161614,"page":12}">*New Gems in Old Letters*</A> says: 

> Letters
> were a place in which Erdős put his mathematical thoughts in progress.
> Theorems are outlined, and new problems are suggested. Because he
> wrote so many letters, his collaborators sometimes never found time to
> follow up on all of these ideas; this leaves us with the rather
> shocking fact that many of Erdős's mathematical ideas are still sitting in
> drawers and filing cabinets of mathematicians around the world. Some of these
> may lead nowhere, but some are likely brilliant insights, still capable of having an
> impact on mathematics today.