1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Modulo 5 problem

  1. Jan 1, 2010 #1
    Well the problem is

    Prove that if x, y, z are intergers such that 5*x^2 + y^2 = 7*z^2, then x, y and z are all divisble by 5.


    So what I have done so far,

    I have worked out 1, 2 ,3 , 4, and their squared to find that. the squared intergers of any interger will end in 0,1, 4 in modulo 5. (ps im not sure if im phrasing this write as well)

    then the LHS would be 0, 1,4. whilst the right hand side will be 0, 2, 3.

    now i dont know wher to go. can someone help me, or show me how to prove this.

    would be greatly appreicated.

    thanks
     
  2. jcsd
  3. Jan 1, 2010 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi doggie_Walkes! :wink:
    Yes! So both sides must be 0, and so … ? :smile:
     
  4. Jan 2, 2010 #3
    Re: Modulo

    thanks tiny tim for replying so quickly.

    well im checked the answer then its says this,

    "the only possiblity is that y=z=0(mod5)

    but then 5*x^2=7*z^2 - y^2 is divisble by 25, and so x is divisble by 5."



    so i get why the obly possiblity is 0mod5 but why is it divisble by 25.

    regards
     
  5. Jan 2, 2010 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi doggie_Walkes! :smile:

    (try using the X2 tag just above the Reply box :wink:)

    ah, because if 5|y and 5|z, then 25|y2 and 25|z2 (and so 25|5x2) :wink:
     
  6. Jan 2, 2010 #5
    Re: Modulo

    Ah tiny tim, I get it! thanks thats bothering for some time, can i ask one more thing of you please. How would one go about doing this?

    5x2+y2 = 7z2

    Deduce that the equation has no solution in intergers except fo x=y=z= 0
     
  7. Jan 2, 2010 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    but that follows directly from the first result …

    think about it! :smile:
     
  8. Jan 4, 2010 #7
    Re: Modulo

    I still dont get it :(
     
  9. Jan 4, 2010 #8

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    5 divides x y and z, so put x = 5a, y = 5b, z = 5c, then 5a2 + b2 = 7c2.

    Now 5 divides a b and c, so put a = 5p, b = 5q, c = 5r, and so on … :smile:
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Modulo problem Date
Finding the Inverse Integer Modulo n Jun 26, 2014
Multiplication modulo algebra Feb 20, 2014
K is a square modulo m? Feb 3, 2013
Modulo reduction problem Feb 27, 2010