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Topic: Factors near the sqrt
Replies: 22   Last Post: Jun 28, 1996 10:49 AM

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Stephen.Donnelly

Posts: 14
Registered: 12/12/04
Factors near the sqrt
Posted: Jun 21, 1996 6:26 AM
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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







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