Question 626170
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Let *[tex \LARGE x] represent the middle number of any given set of three consecutive positive integers.  Then the smaller number of the three is *[tex \LARGE x\ -\ 1] and the larger is *[tex \LARGE x\ +\ 1].  The square of the middle number is *[tex \LARGE x^2] and the product of the smaller and the larger is *[tex \LARGE x^2\ -\ 1].

Note, this is true for all integers, not just the positive integers (what you are calling the "counting numbers")

John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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