From what I can deduce the answer is actually none.

Starting at the boundary condition for where a= b : 1/4002 + 1/4002 = 1/2001 Which reduces to 1/2 + 1/2 = 1 Now for us to move off the boundary condition one of these must grow and the other shrink. Problem is there is no 1/x greater than 1/2 so one can not get any bigger.

Brian Evans

<saxon970@yahoo.com> wrote ... > Hello. I have some questions about how to approach the problem below: > > How many pairs of positive integers a and b are there such that a < b > and > 1/a + 1/b = 1/2001 ? > > End of problem. > > Is trial and error and making a manual list the way to go?