# Colors2

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…xx… P1 ……..xxxxxx…… P2

.E  = —– ……….+…….\$\$\$ __________

………z.. F1 …………………..z…….. F2

About a month ago I wrote about “The Difference of 2 Squares” where it’s discussed how every positive ODD integer can be expressed as the difference of 2 squares. For example:

O = A2 – B2 (where “O” (“Oh” is any Odd positive integer).

You can read that article <here>.

That said, about a week ago I started thinking whether there was a similar statement that could be made about EVEN numbers. For example, a “difference of 2 squares” or something closely related except for EVEN numbers.

What I found is surprising. Interested? If yes then read on…

Lock The Gates!

So, while experimenting with various numbers and “formulas” it quickly surfaced that:

Every positive EVEN integer E can ALWAYS be expressed as the Difference of 2 Squares divided by 2. For example:

A2 – B2E     =     ~~~~~~~~~~

2

This is VERY similar to the Difference of 2 Squares for ODD integers which, again is:

O = A2 – B2

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E  =  P     +     p2 x p3

………… —– …………………. __________

………….F1……………………………..F2

Now is the time for all good men to come to the aid of their 7777777777777777777777777777777.gggg

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