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

 Messages: [ Previous | Next ]
 Bill Taylor Posts: 186 Registered: 11/17/10
Re: Reciprocals of integers summing to 1
Posted: Nov 18, 2012 7:45 AM

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 ?

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.

** No-one has any right to not be offended.
** Neither on their own behalf, their religion, country,
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Date Subject Author
11/16/12 Charlie-Boo
11/16/12 William Elliot
11/16/12 Charlie-Boo
11/16/12 William Elliot
11/17/12 Charlie-Boo
11/18/12 Bill Taylor
11/21/12 David Petry
11/22/12 Bill Taylor
11/22/12 Luis A. Rodriguez
11/22/12 David Petry
11/22/12 David Petry
11/23/12 Bill Taylor
11/23/12
11/23/12 Bill Taylor
11/16/12 Don Redmond
11/16/12 gus gassmann
11/16/12 billh04
11/17/12 Luis A. Rodriguez
11/17/12 Charlie-Boo
11/19/12 Luis A. Rodriguez
11/20/12 doumin
11/22/12 Bill Taylor