[SIZE="3"]Suppose that p and q are odd primes and p=2q+1. Suppose that
α∈ Z_p^*,α≢±1 mod p.
Prove that α is primitive element modulo p if and only if α^q≡-1 mod q.
[SIZE="4"]In RSA: d_K (y)=y^d mod n and n=pq. Define
d_p=d mod(p-1)
d_q=d mod(q-1)
Let
M_p=q^(-1) mod p
M_q=p^(-1) mod q
And
x_p=y^(d_p ) mod p
x_q=y^(d_q ) mod q
x=M_p qx_p+M_q px_q mod n
Show that y^d=x mod n
any help would be appraciated, thanks