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
\(S \left( 1 \right) = 4 \\
S \left( n + 1 \right) = {S \left( n \right)}^2  2 \\
M_p = 2^p  1 \\
n < p, n \in \mathbb{N}, p \in \mathbb{P}\)