thanks for helpin me. guys
1. let p be a prime, show that every prime divisor of (2^p) -1 is greater than p.
2. let n= 3^(t-1). show that 2^n = -1 (mod 3^t)
1. Suppose is a prime divisor of then and thus, by Lagrange's Theorem, the order of divides . (1)
Suppose is the order of , it cannot be 1 for otherwise , and since the order must divide , but since is prime this implies that that is the order of is . So, by (1), thus thus
2. By induction, it's true for k=1, so let's assume it's true for some we'll show that this implies the assertion for
By hypothesis so now: ( see the terms in the binomial expansion), thus:
In fact 2 is a primitive root module for all