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2020-08-22, 20:56   #481
henryzz
Just call me Henry

"David"
Sep 2007
Liverpool (GMT/BST)

10111011010002 Posts

Quote:
 Originally Posted by warachwe Personally, I think these conjectures are interesting in a way that the prove seem somewhat doable, but I agree that we should look more into other phenomena. I think I found a way. S(24k) = 24k-1=(22k-1)(22k+1). 22k+1 is 2 (mod 3) , so there exist a prime p such that p is 2 (mod 3) and p2m-1 divide 22k+1 ,but p2m not divide 22k+1 gcd(22k-1,22k+1)=gcd(2,22k+1)=1, so no other factor of p from 22k-1. Hence p2m-1 preserved 3 for s(24k), so 3 divide s(s(24k))
Brilliant. Now to think about conjecture 3