"David Eppstein" wrote ... | "r.e.s." wrote: | > <email@example.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?