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Old 2020-02-13, 22:33   #4
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Nov 2016

13E16 Posts

Originally Posted by Dr Sardonicus View Post
Remarks on Agrawal's Conjecture indicates the conjecture is likely false.
Yes, it should be false in general (Roman B. Popovych's conjecture could be true however).

Assuming the falsehood of the original conjecture, what I was trying to illustrate is that counterexamples should have very specific properties, namely that the only counterexamples (with r prime) should be Carmichael numbers of order(m) where m = (r-1)/2. There is no proof (that I know of), but there is evidence that this should be true.

There should also exist upper bounds on either the Carmichael numbers of order(m) < x (and show that it is 0 for some x), or there is a lower bound such that the smallest Carmichael numbers of order(m) > L.

If these two arguments are true, then there should exist a modified version of the conjecture that is true as we will have conditions for which n must be prime.

Last fiddled with by carpetpool on 2020-02-13 at 22:33
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