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Some question about number theory

  1. Aug 20, 2011 #1
    How to prove that if a-c | ab+cd then a-c | ad+cb is correct??
    And how to prove the gcd(a^2+b^2, a+b) is 1 or 2. where gcd(a,b)=1.
     
  2. jcsd
  3. Aug 21, 2011 #2
    All I can suggest about the first part is try [itex] (a-c)^2(ab+cd) [/itex]
    That can be written as [itex] a^3b-2a^2bc-2ac^2d+c^3d+ac(ad+cb) [/itex]
    I'm sure I'm lacking some property that can get from here to the solution. Something like, if x divides y and x divides y+z then x also divides z, or similarly, if x divides y and x divides z, then x divides y+z. Properties like that, but I don't think specifically that one, come into play.
     
  4. Aug 21, 2011 #3
    Okay forget what I just said. Try (a-c)(b-d)
     
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