I'm kinda just starting out in this sort of stuff, and i'm rather confused. The professor assigned us to prove these. Not really sure how to start it to be honest. If I could see how these things get solved I think i'll understand it much better.

1. If a and b are 2 positive integers show that gcd(a,b) = gcd(a - b, b)

2. if a and b are 2 positive integers show taht gcd(a,b) = gcd(a, a +b)

3. show that gcd(fn,fn+1) = 1 for all natural numbers n.