Math Is Fun Forum

Synthetic.Butterfly

Member

Registered: 2007-09-25

Posts: 6

How to find something that is x^n and x^y and x^z

I'm trying to solve a problem that requires me to find the smallest number that is x^n and x^y and x^z

In this particular case I'm trying to find a number that is #>2 but #<2 Trillion that is a perfect square, cube and fifth power. I know the answer to the problem however, I don't know how to explain one of my steps. I was wondering if you could help me out?

I know that the answer is 2^30 but how do I explain the 2?

Last edited by Synthetic.Butterfly (2007-09-25 10:54:40)

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: How to find something that is x^n and x^y and x^z

A positive integer that is a square, a cube and a fifth power must be of the form n[sup]lcm{2,3,5}[/sup] = n[sup]30[/sup] for some positive integer n. The smallest such integer > 1 is therefore 2[sup]30[/sup].

Last edited by JaneFairfax (2007-09-25 11:07:22)

Synthetic.Butterfly

Member

Registered: 2007-09-25

Posts: 6

Re: How to find something that is x^n and x^y and x^z

Ok, thanks that answers my question

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: How to find something that is x^n and x^y and x^z

If you define "trillion" as "million million million", then 3^30 and 4^30 would also fit.

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: How to find something that is x^n and x^y and x^z

I normally prefer just to say 10[sup]18[/sup] or 10[sup]12[/sup] as the case may be, instead of using a term with a non-standard definition.
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