A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing

This Question is Closed

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2pn => pa=n for some integer a qn => qb=n for some integer b we want to show pqk=n for some integer k we also have that p and q are two distinct primes if we were to give the prime factorization for n it would look something like p*q*some other prime integers possibly

escolas
 one year ago
Best ResponseYou've already chosen the best response.0And we know that a and b have prime factorizations as well, so we could say that a and b are some product of primes and then that n^2 is pq times some other primes, but how do we know that pq isn't larger than n?

escolas
 one year ago
Best ResponseYou've already chosen the best response.0Oh, is it because if p and q both divide n then they are both part of n? Kinda an Euler's Totient type thing?

myininaya
 one year ago
Best ResponseYou've already chosen the best response.2Yeah since both p and q divide n then we know the prime factorization for n=p*q(some other primes possibly) For example: Let n=972 n=3(324)=2(3)(162)=2^2(3)(81)=2^2*3^5=2*3*(2*3^4) 2972 => 2a=972 3972 => 3b=972 But as we can see in the prime factorization we also have 2*3*k=n

escolas
 one year ago
Best ResponseYou've already chosen the best response.0Thanks, that makes a lot of sense. Much more clear now.

Zarkon
 one year ago
Best ResponseYou've already chosen the best response.1IF you want a more rigorous way you can do the following: since p and q are distinct primes then theie gcd is 1 and so they can be written as a linear combination \[\alpha p+\beta q=1\] and using the notation from above \(n=ap\) and \(n=bq\) we have \[n=n\cdot 1=n(\alpha p+\beta q)\] \[=n\alpha p+n\beta q=bq\alpha p+ap\beta q\] \[=(b\alpha+a\beta)pq\] so \(n\) is an integer multiple of \(pq\). Thus \[pqn\]
Ask your own question
Ask a QuestionFind 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.