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Old 2006-10-20, 23:12   #1
roger's Avatar
Oct 2006

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Default Powers and numbers in sequence

I've been working on various forms to create primes, and came up with one that doen't create primes itself (though a similar one does), but has interesting properties:
n^2-1 = (n-1)(n+1). I expanded this into n^2-x^2 = (n-x)(n+x), and also found n^2+x^2 = (n-x)(n+x)+x.
The cubed form of n then is expressed as n^3-nx^2 = (n-x)(n)(n+x) and n^3+nx^2 = (n-x)(n)(n+x)+2nx^2 .
The first n^4 equation is n^4-4*n^2*x^2-n^2+n-(n-4) = (n-2x)(n-x)(n+x)(n+2x), but I haven't found the equation beginning with n^4+4*n^2*x^2.
Can anyone shed some light on the problem?



PS - equations may not be completely accurate - will verify by next post [signs etc]
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