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2020-03-18, 15:58   #49
BrainStone

Nov 2017
Karlsruhe, Germany

1F16 Posts

Quote:
 Originally Posted by R.D. Silverman Please. This is a math discussion. Learn to state exactly what you mean. When you say "consequently", the obvious reply is "consequently to what?". State mathematically what condition you mean. Math is not "casual English". Do you not know what "order of an element [in a group]" means? It is a fundamental concept that you need to learn. And you also need to learn Lagrange's Theorem if you want to continue further.
Is it possible that $$\exists S \left( n \right) \equiv 1 \mod M_p$$, where
$$S \left( 1 \right) = 4 \\ S \left( n + 1 \right) = {S \left( n \right)}^2 - 2 \\ M_p = 2^p - 1 \\ n < p, n \in \mathbb{N}, p \in \mathbb{P}$$