Comments by "EebstertheGreat" (@EebstertheGreat) on "abc Conjecture - Numberphile" video.

  1. rad(1*2*3) = rad(6) = 2 * 3 = 6 > 3 So it isn't even an exception for k=1.
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  2. rad(2*3*5) = 2*3*5 = 30 > 5 I think you guys didn't understand the video. We want to find a+b=c such that rad(abc)^k < c for some k>1. Actually, to find a true counterexample, we need to find infinitely many (a,b,c) triplets for some particular k satisfying that.
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  3. Note that the conjecture states only that there are finitely many coprime triplets (a,b,c) for which rad(abc)^k > c for each k > 1. There are however infinitely many in total. As k approaches 1 from the right, the number of exceptions increases without bound, so that the union of all (a,b,c) satisfying the inequality for all k > 1 is infinite.
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