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Apr 28, 2013 at 15:51 history edited Suvrit CC BY-SA 3.0
fixed stupid error
Apr 28, 2013 at 15:48 comment added Suvrit Oops, sorry, you are right, it should be $nM^2-m^2$! When typing it up, I felt the $\sqrt{M}$ factor to be a bit odd. Let me update the answer! Thanks.
Apr 28, 2013 at 12:43 comment added alvarezpaiva By the way, it is $s^2 \leq n M^2 - m^2$, right? It makes no difference to the applications I had in mind, because I'm interested in the case $m = M = 1$.
Apr 28, 2013 at 7:04 comment added alvarezpaiva Thanks Suvrit ! Your answer plus the argument to prove the theorem in the OP yields a very neat result (see the edited question).
Apr 28, 2013 at 6:56 vote accept alvarezpaiva
Apr 27, 2013 at 20:43 history answered Suvrit CC BY-SA 3.0