anonymous
  • anonymous
Perfect power question
Meta-math
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions.

anonymous
  • anonymous
Perfect power question
Meta-math
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

anonymous
  • anonymous
For what primes p is \[3^p + 4^p\] a perfect power?
asnaseer
  • asnaseer
for p=2 we get:\[3^2+4^2=5^2\]
anonymous
  • anonymous
yeah 2 is the only even prime too. so you can factor 3^p + 4^p to (3+4) (3^(p-1) - 4 * 3^(p-2) ... + 4^(p-1))

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
but can there be other such primes too?
anonymous
  • anonymous
Other than p = 2, 3^p + 4^p must be divisible by 7 i think
anonymous
  • anonymous
so we lookin for the solutions of this equation\[3^p+4^p=q^n\]p is prime and q,n>1
anonymous
  • anonymous
for p>7 \[3^p+4^p\]is divisible by \(7\) but not by \(7^2\) since\[3^{p-1}-4\times3^{p-2}+4^2\times3^{p-3}-...-3\times4^{p-2}+4^{p-1} \ \ \equiv p3^{p-1} \ \ \text{mod} \ 7\]so there is no solution for p>7 checking for p=2,3,7 gives only solution (p,q,n)=(2,5,2)

Looking for something else?

Not the answer you are looking for? Search for more explanations.