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Old 2020-03-18, 17:59   #52
R.D. Silverman
 
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Nov 2003

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Quote:
Originally Posted by BrainStone View Post
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.
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