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

RolyPoly

Find all positive integer pairs (x,y) such that 4xy-x-y is a perfect square.

  • one year ago
  • one year ago

  • This Question is Closed
  1. mukushla
    Best Response
    You've already chosen the best response.
    Medals 0

    without loss of generality we can suppose \[y\ge x \]because the expression is symmetric

    • one year ago
  2. mukushla
    Best Response
    You've already chosen the best response.
    Medals 0

    assume that \[y=x+a\]with \(a\ge 0\)

    • one year ago
  3. RolyPoly
    Best Response
    You've already chosen the best response.
    Medals 1

    Okay! I'll try from here!!

    • one year ago
  4. mukushla
    Best Response
    You've already chosen the best response.
    Medals 0

    wait ... im afraid i made a mistake :/

    • one year ago
  5. RolyPoly
    Best Response
    You've already chosen the best response.
    Medals 1

    Don't be afraid :P \[4xy-x-y=4x(x+a)-x-(x+a)=4x^2+(4a-2)x-a\]

    • one year ago
  6. RolyPoly
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\Delta=(4a-2)^2 - 4(4)(-a)=0\]\[16a^2 - 16a + 4 + 16a=0\]\[16a^2 + 4 =0\]Well well well...

    • one year ago
  7. shubhamsrg
    Best Response
    You've already chosen the best response.
    Medals 0

    4xy-x-y = (x+y)^2 - (x-y)^2 - (x+y) = (x+y)(x+y-1) - (x-y)^2 i am not too sure if that'd help! :P

    • one year ago
  8. mukushla
    Best Response
    You've already chosen the best response.
    Medals 0

    @RolyPoly ...Are you familiar with modular arithmetic??

    • one year ago
  9. RolyPoly
    Best Response
    You've already chosen the best response.
    Medals 1

    I've never heard of it! :(

    • one year ago
  10. shubhamsrg
    Best Response
    You've already chosen the best response.
    Medals 0

    i dont know much but i do have a little idea..will you please guide me/us through a solution @mukushla

    • one year ago
  11. RolyPoly
    Best Response
    You've already chosen the best response.
    Medals 1

    Forgive me for closing this question, even though it's not yet solved!

    • one year 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.