I think I may be on the verge of something BIG

[Chris Davis]

I don't know if this formula already exists, but I think this may lead to finally finding the fail-proof square-root formula. What I've got now is this:

n^x=n^x-1+n^x-1×(n-1)

I don't know if anyone else has actually discovered the above formula, but I do know that this has never failed for all the n/x combinations i have used. Let me know what you think!

 

[TeethWhitener]

but I do know that this has never failed for all the n/x combinations i have used.

It has never failed, and it never will.$$n^{x-1}+n^{x-1}(n-1) = n^{x-1}+n^{x-1}\times n-n^{x-1}\times 1$$$$=n^{x-1}+n^{x}-n^{x-1}=n^x$$

 

[Chris Davis]

I'm sorry, I'm not a mathmetician. I'm just a high school student. I'm just trying to do the impossible on the off-chance that I might actually discover something. And no, it is NOT April 1.

 

[TeethWhitener]

I'm sorry, I'm not a mathmetician. I'm just a high school student. I'm just trying to do the impossible on the off-chance that I might actually discover something. And no, it is NOT April 1.

Edited out the snark. :P I'll say don't give up, but you may want some guidance. Here's an interesting site I just found that will keep you busy for a while: http://unsolvedproblems.org/

 

[Chris Davis]

Thanks a lot. So that formula that I put up actually WAS already discovered? Just wanting to make sure, so I don't make a fool of myself.

 

[TeethWhitener]

So that formula that I put up actually WAS already discovered?

I wouldn't say it was "discovered" specifically, but it's trivial enough to prove that it isn't really of much interest to mathematicians. However, sometimes little tricks like these allow speedups in physics simulations or other codes (look up 0x5f3759df for a famous example), but you'd have to show that it's better than the existing routines.

 

[Chris Davis]

okay, thanks a lot. I'll keep that in mind. For now, back to my experiments!

 

[Mark44]

It has never failed, and it never will.$$n^{x-1}+n^{x-1}(n-1) = n^{x-1}+n^{x-1}\times n-n^{x-1}\times 1$$$$=n^{x-1}+n^{x}-n^{x-1}=n^x$$

Or, more simply, $n^{x - 1} + n^{x - 1}(n - 1) = n^{x - 1}(1 + n - 1) = n^{x - 1}\cdot n = n^x$

 

[mfb]

I wouldn't say it was "discovered" specifically, but it's trivial enough to prove that it isn't really of much interest to mathematicians.

In other words, if you study physics or mathematics you probably use it as a step in some proof or calculation multiple times without thinking about it.