A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
How do I prove that every powerful number can be written as the product of a perfect square and a perfect cube?
anonymous
 3 years ago
How do I prove that every powerful number can be written as the product of a perfect square and a perfect cube?

This Question is Closed

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Think about it, what do you know about a square?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0there you go thats all it is

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Just curious, but what class is this for?

asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.0how 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
 3 years ago
Best ResponseYou've already chosen the best response.0I didn't really understand the question

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1I was curious because I helped out on the same question yesterday. See http://openstudy.com/study#/updates/50552fcde4b02986d370aedd

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0The first part makes sense but why are u subtracting 3 form ei when ei is odd?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1So 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, \(e_i3\) is even, so \(\displaystyle p_i^{e_i3}=p_i^{f_i}\) is a perfect square.

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Additionally, \(p_i^3\) is a perfect cube.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh that makes perfect sense, thanks alot
Ask your own question
Sign UpFind more explanations on OpenStudy
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
 Engagement 19 Mad Hatter
 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.