r.e.s.
Posts:
400
Registered:
12/4/04


Re: Integer pairs in sum of reciprocals
Posted:
Jan 2, 2001 1:20 AM


"David Eppstein" wrote ...  "r.e.s." wrote:  > <saxon970@yahoo.com> wrote ...  > [...]  >  How many pairs of positive integers a and b are there  >  such that a < b and 1/a + 1/b = 1/2001 ?  > (With c = 2001, I find 14 solutions.)   You apparently forgot about the requirement that a<b.
yup (corrected in a separate posting)
 > I would be interested to know more about the number of  > solutions as a function of c (e.g., asymtotically as c>oo).   It's half the number of divisors of c^2.  So, it doesn't behave very well asymptotically.
When I had earlier plotted the # solutions for 1<=c<=2001, there seemed to be an envelope shaping up that suggested an upper bound that might be very roughly logarithmic. Is the "number of divisors" function, say d(c^2), known to behave anything like that?
r.e.s.

