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