Thread: Conjectured K question View Single Post
2020-03-27, 15:14   #27
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

55316 Posts

Quote:
 Originally Posted by LaurV Then why did you eliminate 9 and 36? (the tree I am barking at, is the fact that 81 is a square)
gd_barnes is right, to extend his post:
to get a riesel/sierpinski cover you have to use d_i divisors in each remainder class in the covering set, you can't use algebraic factors, you can't use even in those cases where you could use, like in your example for k=81 we could cover the n==0 mod 2 case, because 81*1024^n-1 has an algebraic factor. For this reason we can rule out say k=9, it is sure that this sequence contains no prime, but it has no covering set. The proof could be hard/impossible(?), but just see the prime factorization for n=54: http://factordb.com/index.php?id=1100000000033081963 .

ps. you could also cover the n==0 mod 1 so every integer for k=81 with an algebraic factor.

Last fiddled with by R. Gerbicz on 2020-03-27 at 15:17