David Ullrich <email@example.com> 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.