Here are some proofs re primes I need help with
1. Prove that any prime of the form 3n+1 is also of the form 6m+1
2. Show that any integer of the form 3n+2 must have a prime factor of the same form.
3. Show that 7 is the only prime of the form n^3-1
4. Show that p=5 is the only prime for which 3p+1 is a perfect square.
5. If p is prime and p divides a^n, show that p^n divides a^n
6. Show that every integer of the form n^4+4 is composite
Any help gratefully accepted.