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2020-03-18, 17:59   #52
R.D. Silverman

Nov 2003

11100111110112 Posts

Quote:
 Originally Posted by BrainStone Is it possible that $$\exists S \left( n \right) \equiv 1 \mod M_p$$, where $$S \left( 1 \right) = 4 \\ S \left( n + 1 \right) = {S \left( n \right)}^2 - 2 \\ M_p = 2^p - 1 \\ n < p, n \in \mathbb{N}, p \in \mathbb{P}$$
Not if M_p is prime. If M_p is composite then 4 can generate a subgroup.