A difference of squares is an expression of the form 
. It factors according to the algebraic
identity
 |
The algebraic identity holds in every commutative ring, and more generally whenever 
and 
commute.
An integer 
is a difference of two integer squares iff 
. Indeed, 
is a product
of two integers having the same parity.
Conversely, an odd integer 
has the representation
 |
while an integer divisible by 4 can be written 
.
