Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

moneybird Group TitleBest ResponseYou've already chosen the best response.2
For what primes p is \[3^p + 4^p\] a perfect power?
 2 years ago

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

moneybird Group TitleBest ResponseYou've already chosen the best response.2
yeah 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))
 2 years ago

Stom Group TitleBest ResponseYou've already chosen the best response.0
but can there be other such primes too?
 2 years ago

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

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

mukushla Group TitleBest ResponseYou've already chosen the best response.0
for 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)
 2 years ago
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
 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.