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Re^5: Closest factor less than sqrt(N) [proof]

by hv (Parson)
on Feb 21, 2005 at 09:45 UTC ( #432985=note: print w/replies, xml ) Need Help??


in reply to Re^4: Closest factor less than sqrt(N) [proof]
in thread OT: Finding Factor Closest To Square Root

Here's an easier way: take n = m^2, and a factor greater than the square root m + d, then the other factor is:

m^2/(m + d) = m - dm/(m + d) = m - d + d^2/(m + d)
Now d^2/(m + d) is greater than zero, so the cofactor is greater than m - d and hence closer to the square root.

Hugo

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