John Grieve: Diamond Numbers    
 Diamond Numbers4 comments
21 Jan 2016 @ 17:49, by John Grieve


If you square(n+1/2) it becomes n(n+1)+1/4 which can be useful in factorizing numbers. I call these numbers "Diamond Numbers" because n(n+1) is twice a triangular number and two triangles make a diamond.

Diamond numbers can be used in factorization as in the following example:
18=2*9
((5+1/2)-(3+1/2)) * ((5+1/2)+(3+1/2)) = 18

=(5+1/2)squared - (3+1/2)squared = (30+1/4) - (12 + 1/4) = 18 = 2*9

This simple method can be used on much larger numbers and could be part of Fermat's method of factorization based on difference of two squares.

Is this original?



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