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Jan 21, 2013 at 2:09 vote accept Alex G
Jan 20, 2013 at 20:13 answer added Greg Martin timeline score: 7
Jan 20, 2013 at 20:12 comment added Gerhard Paseman You will need fewer than k of them even for that to be possible (which I think is Eric Naslund's point), which will likely be the most prominent condition determining the probability. Even if you study the relaxed condition that no k of the n numbers have a small prime factor in common, I think you will get good bounds on the probability you seek. Gerhard "Ask Me About System Design" Paseman, 2013.01.20
Jan 20, 2013 at 19:50 history edited Greg Martin CC BY-SA 3.0
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Jan 20, 2013 at 18:35 comment added Alex G I thought it was clear that they are chosen at random. Just fixed the possible ambiguity.
Jan 20, 2013 at 18:34 history edited Alex G CC BY-SA 3.0
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Jan 20, 2013 at 18:28 comment added Eric Naslund How are the $x_1,\dots,x_n$ chosen? If they are all multiples of two, then the gcd condition never happens.
Jan 20, 2013 at 18:25 history asked Alex G CC BY-SA 3.0