Question

help please
1/ Let a ∈Z, a not equals 0. prove gcd(a,0) = |a|.
2/ For a,b ∈Z (not both 0). prove gcd(a,b) = gcd(b,a).

Answer 1

For the first one shouldn't it be enough to say a=|a|*sign(a) and 0=|a|*0
sign(a) can be -1 or 1
recall the definition of gcd(a,b) is max{d : d|a and d|b}
and |a|>0 so gcd(a,0) is |a|.... I don't see much to prove honestly. :(

and for the second one I think you would just need to prove an and statement is commutative for example show A and B is the same as B and A since the def of gcd(a,b) is max{d: d|a and d|b}