Question

What conjectures are there concerning differences of squares?

Answer 1

`a^2-b^2=(a+b)(a-b)`

Explanation:

`a^2-b^2=(a+b)(a-b)`

We can prove this by simply expanding `(a+b)(a-b)`:
`(a+b)(a-b)`
`=a^2-ab+ab-b^2`
`=a^2-b^2`

Answer 2

A few thoughts...

Explanation:

Most properties of differences of squares seem to be fairly straightforward to prove. I suppose if you did not know the proofs then they would be conjectures. For example:

• Any odd number is the difference of squares of two integers.

• Any multiple of `4` is the difference of squares of two integers.

• Any integer of the form `4k+2` (where `k` is an integer) is not the difference of squares of two integers.