What conjectures are there concerning differences of squares?

2 Answers
Y
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#

George C.
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.

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