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From: Bill Dubuque on 5 Feb 2010 16:01
ksoileau <kmsoileau(a)gmail.com> wrote:
>
> Proof or counterexample, please:
>
> Every rational between 0 and 1 can be written as a sum of reciprocals
> of distinct positive integers. If the fractions are sorted in
> increasing denominator order, this representation is unique. For
> example: 131/483 = 1/3+1/7+1/483.

HINT they're never unique since 1/n = 1/(n+1) + 1/(n(n+1))

Googling "Egyptian fraction" reveals much literature.

--Bill Dubuque
From: Gerry on 5 Feb 2010 16:54
On Feb 6, 7:30 am, James Dow Allen <jdallen2...(a)yahoo.com> wrote:

> I think there's an unresolved conjecture by Erdos that
>         4/n = 1/a + 1/b + 1/c
> has solutions for all n > 1.

Erdos and Straus, if I'm not mistaken. Certainly included in
Guy's Unsolved Problems In Number Theory.
--
GM
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