Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Mr.Math Group Title

Find all integers a,b for which \(a^4+4b^4\) is a prime.

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 7

    a=b=1 is the only possible solution.

    • 2 years ago
  2. Mr.Math Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Could you prove your claim? :-P

    • 2 years ago
  3. Hero Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah FFM

    • 2 years ago
  4. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 7

    Yes I definitely can ... why you don't believe me MR.Math? :(

    • 2 years ago
  5. Mr.Math Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    lol, I do believe you! Where did I say that I don't? :-(

    • 2 years ago
  6. Hero Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    FFM, stop stalling and post the proof :P

    • 2 years ago
  7. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 7

    hehe, okay here it goes, \[ a^4+4b^4= ((a+b)^2+b^2) \times ((a-b)^2+b^2)) \] Now, \( ((a+b)^2+b^2) \gt 1\) (always) so for \( a^4+4b^4 \) to be prime \((a-b)^2+b^2) =1\) and this can only happen when \(a=b=1\) (QED)

    • 2 years ago
  8. Mr.Math Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Awesome! I've always believed in you son :-)

    • 2 years ago
  9. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 7

    Haha, how old are you man? :D

    • 2 years ago
  10. Mr.Math Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Very old.

    • 2 years ago
  11. Hero Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    FFM, how do you come up with such approaches to proofs?

    • 2 years ago
  12. FoolForMath Group Title
    Best Response
    You've already chosen the best response.
    Medals 7

    Hero, I really wonder that myself ...

    • 2 years ago
    • Attachments:

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.