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Topic: Reciprocals of integers summing to 1
Replies: 21   Last Post: Nov 23, 2012 8:44 PM

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Bill Taylor

Posts: 186
Registered: 11/17/10
Re: Reciprocals of integers summing to 1
Posted: Nov 18, 2012 7:45 AM
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Quite clearly a lot of respondents didn't seem to read the question!

> For each n, what are the solutions in positive integers
> to (1/X1)+(1/X2) + . . . + (1/Xn)=1 ?

Admittedly no comment was made on permutations of solutions,
but in such contexts they are almost always regarded as the same.

Clearly repeats among the x_i are allowed.
(Though one could also answer with them disallowed.)

But most important, A FUNCTION OF n IS REQUIRED.

i.e. what is f(n) = card({x1, x2, ... , xn} | etc)

where the curly brackets denote unordered multisets.

So far we have f(1) = 1, f(2) = 1, f(3) = 3 (seemingly)
and no great effort on any higher values.

If no-one can get anywhere much theoretically,
can some computer whizz at least produce a list of
the first several values of f please?

-- Whacking Willy.

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