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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
Re: Factors near the sqrt
Posted: Jun 24, 1996 1:14 AM
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David Ullrich <ullrich@math.okstate.edu> wrote:
> Peter Montgomery wrote:
>> If N = xy where x and y are integers and x is bounded as above,
>> then show that
>>
>> 0 <= x + y - 2*sqrt(N) < 1.

>
> How does this go? If I perform the obvious sorts of manipulations
>I get inequalities much weaker than this. Not that that proves anything.
>


Well, I did it by finding the range of the function
f(x) = x + y = x + N/x
in the relevant interval,
although there may be a better way.

Steve







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