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

1. Prove that the fraction is in lowest terms for every positive integer

2. Let , show that

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

4. Show that can never be an integer. (I'm thinking of showing converges to a value... or something along those lines, probs wrong heh)

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