as stated in the title - Find the smallest integer k such that 600k is a cube number. Thanks ever so much!

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- May 14th 2009, 12:08 PMBabyMilo[Solved] Find the smallest integer k such that 600k is a cube number.
as stated in the title - Find the smallest integer k such that 600k is a cube number. Thanks ever so much!

- May 14th 2009, 12:14 PMMoo
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 - May 14th 2009, 12:16 PMIsomorphism
- May 14th 2009, 12:35 PMBabyMilo
Fully understood! Thanks both of you!