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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.
** No-one has any right to not be offended.
** Neither on their own behalf, their religion, country,
** football team nor anything else!
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