[seqfan] A conjecture of Saha and Karthik.

L. Edson Jeffery lejeffery2 at gmail.com
Thu Feb 13 02:18:47 CET 2014


While reading about the Wall-Sun-Sun prime conjecture, I ran across the
following conjecture by Saha and Karthik on the last page of their preprint
http://arxiv.org/abs/1102.1636 :


For n a positive integer, let pi(n) denote the least positive integer k
such that n | F(k) and F(k+1) == 1 (mod n), where F(m) is the m-th
Fibonacci number (pi(n) is sometimes called the 'Pisano period'). Let S
denote the set of all solutions of pi(n^2) = pi(n) over the positive
integers. Then S = {6,12}.


S is reminiscent of the recent A235383 = {8,144}. Is there a deeper
relation between the two sequences, and should the conjectured S be
included in the database?

Ed Jeffery


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