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Difference of square no.s

  1. Sep 14, 2008 #1
    is there an expression for the difference of two square no.s, except, of course for rsquare minus ssquare
     
  2. jcsd
  3. Sep 14, 2008 #2
    (r+s)(r-s)
     
  4. Sep 14, 2008 #3
    god you are funny. i posted this question because i was trying to find out all possible no.s which have a self-conjugating ferrer's graph, and needed to see if diff. of two square no.s is in anyway in form of a triangle no. or not. anyways, i have inferred that all no.s except for 2 can be jotted as a self-conjugating ferrer's graph. am i correct?
     
  5. Sep 14, 2008 #4

    CRGreathouse

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    Your first post was entirely unclear, and I'm not quite sure what your second means. "if diff. of two square no.s is in anyway in form of a triangle no. or not"? Does that mean something like "Is the difference of two squares triangular?"?

    If that interpretation is generally correct, I can think of at least four ways to take it:
    [tex]\forall n>m \exists t:t(t+1)/2=n^2-m^2[/tex]
    [tex]\forall n \exists m,t:t(t+1)/2=n^2-m^2[/tex]
    [tex]\forall N \exists n>m>N,t:t(t+1)/2=n^2-m^2[/tex]
    [tex]\exists n,m,t:t(t+1)/2=n^2-m^2[/tex]

    If it's not, then you'll have to be more clear.
     
  6. Sep 15, 2008 #5
    that was exactly what i meant, so thanks
     
  7. Sep 15, 2008 #6

    CRGreathouse

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  8. Sep 15, 2008 #7
    the first one. by the way, am i not correct in saying that all +ve integers except 2 can be expressed as a self conjugating ferrer's graph?
     
  9. Sep 15, 2008 #8

    CRGreathouse

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    The first few (n, m) for which this fails are:
    (3, 1)
    (5, 1)
    (3, 2)
    (4, 2)
    (4, 3)
    (5, 3)
    (5, 4)
     
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