
Re: Reciprocals of integers summing to 1
Posted:
Nov 17, 2012 4:19 PM


On Nov 16, 2:52 am, William Elliot <ma...@panix.com> wrote: > On Thu, 15 Nov 2012, CharlieBoo wrote: > > On Nov 16, 12:21 am, William Elliot <ma...@panix.com> wrote: > > > On Thu, 15 Nov 2012, CharlieBoo wrote: > > > > For each n, what are the solutions in positive integers (or in > > > > integers) to (1/X1)+(1/X2) + . . . + (1/Xn)=1 ? > > > > x1 = x2 =..= x_n = n > > > But there is also 1/2 + 1/3 + 1/6 = 1. I am asking for all solutions. > > 1/3 + 1/2 + 1/6 > 1/6 + 1/3 + 1/2, > etc., > for a total of 6 + 1. > > Do I hear more? > >
Start with {1}, a set containing N elements including N! . Replace N! with (N+1)!/N and (N+1)! to create another such set.
CB

