Thread: proof [(a,b),c]=([a,c],[b,c])...?

I can't prove ...if a,b,c are positive integer, then

1.) [(a,b),c]=([a,c],[b,c])

2.) ([a,b],c)=[(a,c),(b,c)]


.....*-*!!

Originally Posted by konna

I can't prove ...if a,b,c are positive integer, then

1.) [(a,b),c]=([a,c],[b,c])

2.) ([a,b],c)=[(a,c),(b,c)]


.....*-*!!

I'm afraid you are going to have to define [x,y] and (x,y).

Originally Posted by konna

I can't prove ...if a,b,c are positive integer, then

1.) [(a,b),c]=([a,c],[b,c])

2.) ([a,b],c)=[(a,c),(b,c)]


.....*-*!!

Oh!1 sorry sorry!
[(a,b),c]=([a,c],[b,c])=>lcm[gcd(a,b),c]=gcd(lcm[a,c],lcm[b,c])


([a,b],c)=[(a,c),(b,c)]=>gcd(lcm[a,b],c)=lcm[gcd(a,c),gcd(b,c)]