20061020, 23:12  #1 
Oct 2006
404_{8} Posts 
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^21 = (n1)(n+1). I expanded this into n^2x^2 = (nx)(n+x), and also found n^2+x^2 = (nx)(n+x)+x. The cubed form of n then is expressed as n^3nx^2 = (nx)(n)(n+x) and n^3+nx^2 = (nx)(n)(n+x)+2nx^2 . The first n^4 equation is n^44*n^2*x^2n^2+n(n4) = (n2x)(nx)(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] 
20061023, 09:58  #2  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Expansions
Quote:
Quote:
Mally 

20061023, 15:55  #3 
Oct 2006
2^{2}×5×13 Posts 
First of all, sorry for the erroneous data to you who have worked on this.
Here are all the ones I have that are proven: ^2 : n^2x^2 = (nx)(n+x); n^2+x^2 = (nx)(n+x)+x ^3 : n^3n*x^2 = (nx)(n)(n+x); n^3+nx^2 = (nx)(n)(n+x)+2n*x^2 ^4 : n^45n^2*x^2+4x^4 = (n2x)(nx)(n+x)(n+2x); n^4+5n^2*x^2+4x^4 = (n2x)(nx)(n+x)(n+2x)+10n*x^2 ^5 : n^55n^3*x^2+4n*x^4 = (n2x)(nx)(n)(n+x)(n+2x); n^5+5n^3*x^2+4n*x^4 = (n2x)(nx)(n)(n+x)(n+2x)+10n^3*x^2 At the moment, ^6 is not on there because, even though I have double and checked again, whenever I enter a value for the equation I came up with (double checking the work behind it too), I get a negative or zero value, or at least ones that don't fit the approximated values. I will continue trying to fix this one, and will write back quicker than last time. Thanks to all those who attempted and wrote back, and I hope I haven't taken up too much of your time with my bad equations. Roger PS  mfgoode  n^2+1 often/always comes up with primes. Will look back into this also Last fiddled with by roger on 20061023 at 15:56 
20061024, 22:50  #4 
Oct 2006
2^{2}·5·13 Posts 
I checked back on n^6, and discovered I'd been thinking backwards, so confused after working pages of bad data that (obviously) gave no results.
For n^6 though, I have come to another stumbling block. All I have discovered is that for at least x<4 (exclusive), the difference between the right hand side of the equation [(nx)(n+x) for n^2] and the left [n^2*x^2 for n^2] is divisible by 7. My method for finding n^a+ (probably slow) is to obtain n as well as the right side of the equation, giving a value, and subtracting that value from the left side to obtain a new value (I'll call this b). a is then some form or other (the rightmost bit of the right side), but with n^6+, all I know/can see is that b/y is a whole number (and then can be further broken down into a form of some kind, like the other a's) Can anyone advise? Thanks, Roger 
20061025, 01:37  #5 
"William"
May 2003
New Haven
2^{2}·3^{2}·5·13 Posts 

20061026, 22:31  #6 
Oct 2006
2^{2}·5·13 Posts 
Sorry
Sorry about all that, I realized how all my attempts were clouded by forgetting math class (factoring etc.). Next post I make will have relevence.
Roger 
20061027, 11:52  #7  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}×3^{3}×19 Posts 
The Binomial.
Quote:
Roger, study the masters first before you can become one yourself. I would advise you to study and master the Binomial Theorem in its entirety. I gather you dont have a clue about it. In passing, it is not obligatory to post a thesis of your own. You can always learn by asking questions until you can stand on your own two feet. Read every post as far as possible and whatever is in your range of interests. The forum has a wide variety of topics so you can pick your posts Best of luck, Mally 

20061027, 21:54  #8 
Oct 2006
2^{2}×5×13 Posts 
Thanks, mally
I'll look into it, and take your advice Roger 
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