Hi guys, help me out with these, please!

1. if p is a prime satisfying n<p<2n, show that

2n(2n-1).....(n+1) / n(n-1)(n-2).....1 = 0(mod p)

2. If gcd(a, 35)=1, show that a^12 = 1(mod 35)

3. If p and q are distinct primes, prove that

p^(q-1) + q^(p-1) = 1 (mod pq)

Thanks so much!

bEST WISHES,