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2006-10-23, 09:58   #2
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

80416 Posts
Expansions

Quote:
 Originally Posted by roger 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? Thanks, Roger PS - equations may not be completely accurate - will verify by next post [signs etc]
Kindly correct your expressions as some of them are wrong then we can get somewhere.

Quote:
 Originally Posted by roger "(though a similar one does), but has interesting properties:"
Which one??

Mally