prove that <x^m> intersection <x^n> = <x^LCM(m,n)>
The Attempt at a Solution
let b be in <x^n> intersection <x^m>
then for some t,k,p in Z, b=x^(mt) = x^(nk) thus b=x^(LCM(m,n) * p i.e. b is in <x^LCM(m,n)>
let b be in <x^LCM(m,n)>
let s=lcm(m,n) =mt=nk for some t,k in Z
then for some r in Z , b=x^(sr)
then b = x^(mt)r =x^(nk)r
and that's where I'm stuck..
I was also considering trying to find and isomorphic mapping from one set to another..