as stated in the title - Find the smallest integer k such that 600k is a cube number. Thanks ever so much!
Hello,
The trick for this is to factor 600 :
But in a cube number, the prime decomposition is in the form
So for , it's okay.
If 3 is in the prime decomposition of the cube number, then has to. So keep a factor
Same reasoning for 5. Keep a factor 5.
is the smallest integer such that is a cube number.
This is a rather intuitive thing. I'm sorry if I'm not providing a formal proof :s