I just started self learning basic number theory so please excuse me for any noob questions:

1. Prove that the fraction http://stuff.daniel15.com/cgi-bin/ma...E4+3n%5E2+1%7D is in lowest terms for every positive integer http://stuff.daniel15.com/cgi-bin/ma...%5Cmbox%7Bn%7D

2. Let http://stuff.daniel15.com/cgi-bin/ma...Cmathbb%7BN%7D, show that http://stuff.daniel15.com/cgi-bin/ma...29%28c,a%29%7D

3. Prove that consecutive Fibonacci numbers are always relatively prime.

4. Show that http://stuff.daniel15.com/cgi-bin/ma...%7B1%7D%7Bn%7D can never be an integer. (I'm thinking of showing http://stuff.daniel15.com/cgi-bin/ma...%7B1%7D%7Bk%7D converges to a value... or something along those lines, probs wrong heh)

Can anyone show me how to do these questions? Thank you.