anonymous
  • anonymous
How do I prove that every powerful number can be written as the product of a perfect square and a perfect cube?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Think about it, what do you know about a square?
anonymous
  • anonymous
they are even
anonymous
  • anonymous
there you go thats all it is

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KingGeorge
  • KingGeorge
Just curious, but what class is this for?
asnaseer
  • asnaseer
how does that prove it? I didn't know what "powerful numbers" were until I just looked them up. if I understand it correctly then a powerful number is a positive integer m such that for every prime number p dividing m, p^2 also divides m.
anonymous
  • anonymous
Proofs class
anonymous
  • anonymous
I didn't really understand the question
asnaseer
  • asnaseer
:/
KingGeorge
  • KingGeorge
I was curious because I helped out on the same question yesterday. See http://openstudy.com/study#/updates/50552fcde4b02986d370aedd
anonymous
  • anonymous
The first part makes sense but why are u subtracting 3 form ei when ei is odd?
KingGeorge
  • KingGeorge
So that I get \[\large p_i^{e_i}=p_i^{f_i+3}=p_i^{f_i}\cdot p_i^3\]Note that since \(e_i\) is odd, \(e_i-3\) is even, so \(\displaystyle p_i^{e_i-3}=p_i^{f_i}\) is a perfect square.
KingGeorge
  • KingGeorge
Additionally, \(p_i^3\) is a perfect cube.
anonymous
  • anonymous
oh that makes perfect sense, thanks alot
KingGeorge
  • KingGeorge
You're welcome.

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