For all k>0,k∈ℤ . Prove

I think I understand what this wants but i can't figure out how to set up a formal proof. These are the guidelines we have to follow http://i.imgur.com/qpIYqPp.pnggcd(k∗a,k∗b)=k∗gcd(a,b)

Can anyone help me figure this out

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- Apr 21st 2014, 07:59 PMshmiksstruggling with proof: gcd(k∗a, k∗b)=k∗gcd(a, b)
For all k>0,k∈ℤ . Prove

I think I understand what this wants but i can't figure out how to set up a formal proof. These are the guidelines we have to follow http://i.imgur.com/qpIYqPp.pnggcd(k∗a,k∗b)=k∗gcd(a,b)

Can anyone help me figure this out - Apr 21st 2014, 08:14 PMSlipEternalRe: struggling with proof: gcd(k∗a, k∗b)=k∗gcd(a, b)
Any time you are working with gcd, you will probably want to start with terms of the form $\displaystyle kax+kby$. You might even want to consider the set $\displaystyle A = \{kax+kby\in \mathbb{N} \mid x,y \in \mathbb{Z}\}$. The minimum of that set is the gcd. Next show that the right hand side produces a divisor of both ka and ka. Then show it produces a greatest divisor.