Blog Entries: 2

## difference of square no.s

is there an expression for the difference of two square no.s, except, of course for rsquare minus ssquare
 (r+s)(r-s)
 Blog Entries: 2 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?

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## difference of square no.s

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:
$$\forall n>m \exists t:t(t+1)/2=n^2-m^2$$
$$\forall n \exists m,t:t(t+1)/2=n^2-m^2$$
$$\forall N \exists n>m>N,t:t(t+1)/2=n^2-m^2$$
$$\exists n,m,t:t(t+1)/2=n^2-m^2$$

If it's not, then you'll have to be more clear.
 Blog Entries: 2 that was exactly what i meant, so thanks
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 Blog Entries: 2 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?

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 Quote by chhitiz the first one.
 Quote by CRGreathouse $$\forall n>m \exists t:t(t+1)/2=n^2-m^2$$
The first few (n, m) for which this fails are:
(3, 1)
(5, 1)
(3, 2)
(4, 2)
(4, 3)
(5, 3)
(5, 4)