1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solve explicitly integer solution

  1. Sep 17, 2010 #1
    1. The problem statement, all variables and given/known data

    find p,q,r,s integer solution

    [tex]\frac{1}{p^2}+\frac{1}{q^2}+\frac{1}{r^2}+\frac{1}{s^2}=1[/tex]

    2. Relevant equations

    here some alternate form you can see

    http://www.wolframalpha.com/input/?i=1/p^2%2B1/q^2%2B1/r^2%2B1/s^2%3D1

    3. The attempt at a solution

    i don't know if this works,

    so i guess i have to show that [tex]p=q=r=s[/tex],

    so now i only got this [tex]p|(qrs)^2\ \ ,\ q|(prs)^2\ \ ,\ r|(pqs)^2\ \ ,\ s|(pqr)^2[/tex], but i dont even know how to show [tex]p|q[/tex]

    help T_T
     
  2. jcsd
  3. Sep 17, 2010 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You should just do a size comparison

    One side is: Can any of p, q r or s be equal to 1?

    And then the flip side: What happens if p is a large integer (how are the possible sizes for q, r and s restricted)
     
  4. Sep 17, 2010 #3
    it can't, i'll show to you to check my proof of this later

    hmm, do you mean p>2??

    if yes, i only get [tex]\frac{1}{q^2}+\frac{1}{r^2}+\frac{1}{s^2} < \frac{1}{2}[/tex] how to get restriction on p,q,r?
     
  5. Sep 17, 2010 #4

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If p>2, you should get the inequality [tex]\frac{1}{q^2}+\frac{1}{r^2}+\frac{1}{s^2}>\frac{3}{4}[/tex]
     
  6. Sep 17, 2010 #5
    yeaa thats true, maybe i don't understand the flip flip side thing. very sleepy, i'll try understand it tomorrow. anyway, what should i do next?

    assume some more what happen if q>2 ??
     
  7. Sep 17, 2010 #6

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Well, if none of q,r and s are 1, what's the largest [tex] \frac{1}{q^2} + \frac{1}{r^2}+\frac{1}{s^2}[/tex] can be?
     
  8. Sep 17, 2010 #7
    sorry i still don't get it

    hmm, i guess there's nothing to do with post 3 and 4,

    this is what i understand p,q,r,s can't be 1

    if p>1 then largest [tex] \frac{1}{q^2} + \frac{1}{r^2}+\frac{1}{s^2}[/tex] is 3/4

    then? ;P
     
  9. Sep 17, 2010 #8

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Use what's in post number 4 (which you should work on solving for: why don't you post your attempt at it?)
     
  10. Sep 17, 2010 #9
    aahhh, maybe i see now,

    so p=q=r=s=2 is a solution.

    so that we goin through is showing that p not equal 2 in Z+ is not a solution.

    also i have to repeat for q,r and s right?
     
  11. Sep 17, 2010 #10

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    If there is a solution for which q (or r or s) is not equal to 2, you should be able to prove in a line or two that a solution exists for which p is not equal to 2 (which gives a contradiction of course)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solve explicitly integer solution
  1. Solve y explicitly (Replies: 14)

  2. Integer solution (Replies: 14)

Loading...