Need proofs for the following lemmas:

- Let a, b, c belong to Z (integers) and suppose gcd(c,a)=1. If c|ab implies c|b.
- Let a,b,q,r belong to Z with a=qb+r, then

3. Let x,y,z belong to Z. Then gcd (x,y,z)=1 IF AND ONLY IF gcd(x,y) and gcd (x,z)=1

- gcd(a,b)=gcd(b,r)
- gcd(a,b)=gcd(-a,b)=gcd(a,-b)=gcd(-a,-b)