Re: Egyptian fractions conjecture.

In article <1161319757.892561.29660@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Bill Taylor" <w.taylor@xxxxxxxxxxxxxxxxxxxxx> wrote:

This matter was raised a month or so ago, but I don't recall
seeing a reply. Apologies if I missed one.

There are some conjectures about Egyptian fractions,
by (I think) Erdos, or perhaps Seirpinski. They relate
to whether there is a global upper bound on the number of
Egyptian fractions required to sum to an arbitrary given
rational between 0 and 1.

Can anyone please give

(i) the author(s) and statement(s) of the conjecture(s).
(ii) their current status.

Erdos & Straus conjectured 4 / n is a sum of three unit fractions
for all n > 1. Unsolved. Numerically verified into the billions.

Sierpinski conjectured the same for 5 / n. Unsolved. Numerically
verified into the billions.

Lots of info under Problem D11 in Guy, Unsolved Problems in
Number Theory.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.