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Prove property of diophantine equation

  1. Oct 17, 2004 #1
    Show that the diophantine equation x^2 - y^2= n is solvable in integers iff n is odd or 4 divides n.
  2. jcsd
  3. Oct 18, 2004 #2
    Well, 4^2-3^2=7 and 4^2-2^2=12, 12/4=3.
  4. Oct 19, 2004 #3

    matt grime

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    That isn't a proof. That is an example.

    Consider the answer mod 4, one only needs to show n =2 mod 4 can't happen, which is straight forward.
  5. Oct 19, 2004 #4


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    And it becomes all the more obvious if you write x = y + k, for some integer k.

    Edit : Well, maybe not...but it doesn't make it harder.
    Last edited: Oct 19, 2004
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