A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Perfect power question
anonymous
 4 years ago
Perfect power question

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0For what primes p is \[3^p + 4^p\] a perfect power?

asnaseer
 4 years ago
Best ResponseYou've already chosen the best response.0for p=2 we get:\[3^2+4^2=5^2\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah 2 is the only even prime too. so you can factor 3^p + 4^p to (3+4) (3^(p1)  4 * 3^(p2) ... + 4^(p1))

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but can there be other such primes too?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Other than p = 2, 3^p + 4^p must be divisible by 7 i think

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so we lookin for the solutions of this equation\[3^p+4^p=q^n\]p is prime and q,n>1

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0for p>7 \[3^p+4^p\]is divisible by \(7\) but not by \(7^2\) since\[3^{p1}4\times3^{p2}+4^2\times3^{p3}...3\times4^{p2}+4^{p1} \ \ \equiv p3^{p1} \ \ \text{mod} \ 7\]so there is no solution for p>7 checking for p=2,3,7 gives only solution (p,q,n)=(2,5,2)
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.