Difference of square no.s

1. Sep 14, 2008

chhitiz

is there an expression for the difference of two square no.s, except, of course for rsquare minus ssquare

2. Sep 14, 2008

huba

(r+s)(r-s)

3. Sep 14, 2008

chhitiz

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?

4. Sep 14, 2008

CRGreathouse

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.

5. Sep 15, 2008

chhitiz

that was exactly what i meant, so thanks

6. Sep 15, 2008

CRGreathouse

Which?

7. Sep 15, 2008

chhitiz

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?

8. Sep 15, 2008

CRGreathouse

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