
Factors near the sqrt
Posted:
Jun 21, 1996 6:26 AM


I thought this was a straightforward matter, but it's causing me some trouble.
Is this proposition true?
PROPOSITION: Given any natural number N, the number of factors of N in the set {x : N^(1/2) \le x \le N^(1/2)+N^(1/4)} is at most 1.
If not, is there a similar fact, with a smaller range?
If so, does anyone have a neat proof, or a good reference?
In either case, is this related to a more general problem concerning the distribution of factors of N near some given M < N ?
Any help will be much appreciated.
Steve

