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Oct 30, 2010 at 23:45 comment added Jérôme JEAN-CHARLES Assuming this is an heuristic argument, I still have a problem with this when using a serie: I feel you are making some regularity assumption that you do not specify. In fact there could be very very few $n$ - yet an infinite number- ( like one every triple exponential) that will not change the serie convergence and not by much. Could you specify that "regularity" or "independence".
Sep 21, 2010 at 5:50 comment added Alexey Ustinov Probabilistic arguments are clear. They are even more powerful than $abc$-conjecture.
Sep 20, 2010 at 17:04 comment added Dror Speiser The probability that N(N+1) is divisible by 3 is not 1/3, then shouldn't this also be accounted for?
Sep 20, 2010 at 12:13 comment added Denis Serre @Chris. Yes I did. Thanks for the correction.
Sep 20, 2010 at 12:12 history edited Denis Serre CC BY-SA 2.5
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Sep 20, 2010 at 11:30 comment added Chris Wuthrich Did you mean $N = [\sqrt{n!}]$ in the first line ?
Sep 20, 2010 at 6:38 history answered Denis Serre CC BY-SA 2.5