What conjectures are there concerning differences of squares?

2 Answers
May 14, 2017

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

May 14, 2017

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.