Odd and Even Multiplicative Orders
- As part of the search for Brier numbers for bases other than 2, I have
observed (although for only one base b=12), that primes that have an
even multiplicative order base 12 may contribute to cover sets for
both Sierpinski and Riesel numbers, and therefore for Brier numbers;
whereas odd multiplicative order primes can contribute to Sierpinski
or Riesel covers, but not both at the same time.
A worked example is shown at
http://www.mersenneforum.org/showthread.php?t=10930 post 16
I wonder why that is? Can someone provide some maths on that. Is it
the case for all bases?