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#1 2010-07-30 04:49:31

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,585

3 numbers in a row multiplied

2 x 3 x 4 = 24 and 3 x 3 x 3 = 27 and 27 - 3 = 24

3 x 4 x 5 = 60 and 4 x 4 x 4 = 64 and 64 - 4 = 60

1 x 2 x 3 = 6 and 2 x 2 x 2 = 8 and 8 - 2 = 6

4 x 5 x 6 = 120 and 5 x 5 x 5 = 125 and 125 - 5 = 120

This can be proven with the difference of two squares...

(n-1)(n)(n+1) = (n^2-1)n, which is n less than n^3.


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