Arnold Williams (notebuyer) wrote,
Arnold Williams
notebuyer

The Difference of Squares: Parity Note

Difference of Squares x^2 - a^2 has a shortcut in (x+a)*(x-a). For some applications, which employ a parity check, there is a shortcut to that, too.

If (x-a) is an odd number, the difference of squares will be odd, and if it is an even number, the difference of squares will be even.

Elementary result of the sequence of squares, all of which consecutive squares are separated by an odd number, and if we start at 1, they are all separated by the odd integers in order, see prior proofs.
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