Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ashur Group Title

How do I prove that every powerful number can be written as the product of a perfect square and a perfect cube?

  • one year ago
  • one year ago

  • This Question is Closed
  1. ilikephysics2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Think about it, what do you know about a square?

    • one year ago
  2. ashur Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    they are even

    • one year ago
  3. ilikephysics2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    there you go thats all it is

    • one year ago
  4. KingGeorge Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Just curious, but what class is this for?

    • one year ago
  5. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    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.

    • one year ago
  6. ashur Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Proofs class

    • one year ago
  7. ilikephysics2 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I didn't really understand the question

    • one year ago
  8. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    :/

    • one year ago
  9. KingGeorge Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I was curious because I helped out on the same question yesterday. See http://openstudy.com/study#/updates/50552fcde4b02986d370aedd

    • one year ago
  10. ashur Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The first part makes sense but why are u subtracting 3 form ei when ei is odd?

    • one year ago
  11. KingGeorge Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    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.

    • one year ago
  12. KingGeorge Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Additionally, \(p_i^3\) is a perfect cube.

    • one year ago
  13. ashur Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh that makes perfect sense, thanks alot

    • one year ago
  14. KingGeorge Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You're welcome.

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.