i need a hint please help
Show that every positive integer n can be written uniquely in the form n=ab, where a is a square-free and b is a square. Show that b is then the largest square dividing n.
If n is square-free, then a=n and b=1
If n is a square, then a=1 and b=n
If n is not square free, nor a square, it means that there exists integers m>1 and k>1 such that
If k is square free, then you are done : b=mē and a=k
If k is not square free, then there exists integers p>1 and q>1 such that
If q is square free...
If q is not square free...
And so on...