Question

Prove the gcd(m,n)=gcd(-m,-n). So far have:
Let gcd(m,n)=k
Then k=am+bn=min{sm+tn; s,t are integers}.
May not have even started correctly...

Answer 1

\[\text{ http://en.wikipedia.org/wiki/Euclidean_algorithm }\]

Answer 2

On observation, if you take -1 out from both -m and -n you end up with m and n, implying that the gcd should be the same.

Answer 3

gcd is greatest common divisor of m and n right?

Answer 4

to prove it, you might want to start by expressing it symbolically in propositional logic, and determining what your proving methods would look like. Direct, contraposition, and contradiction are the 3 that i am aware of

Answer 5

thanks, i got it!