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September 19th, 2018, 12:24 PM   #1
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Hmmm...

n^4 - n^3 + n^2 - n = n*{n*[n*(n - 1) + 1] - 1}

Just got that...kinda accidentally...mean anything?
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September 19th, 2018, 01:06 PM   #2
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Quote:
Originally Posted by Denis View Post
n^4 - n^3 + n^2 - n = n*{n*[n*(n - 1) + 1] - 1}

Just got that...kinda accidentally...mean anything?
It means you expanded the right side of the equation?
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September 19th, 2018, 02:43 PM   #3
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Okay, I was being mildly facetious in my first reply. I would like to know how you happened upon that.

If you expand from the inside out, starting with what's inside the square brackets, you have:

n^2 - n + 1

Next step out - the curly brackets:

n^3 - n^2 + n - n

And that's the key step. You've got the +n and -n, which are already zero if you're going to do anything else to that entire string.

So the key to this seems to be including +1 inside the square brackets, but external to the parentheses, and then including -1 inside the curly brackets but external to the square brackets. Since you're essentially multiplying each 'group'' successively by n, then you've guaranteed producing a +n and a -n by that setup.

Was there something else there that you saw or wondered about?
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September 19th, 2018, 02:52 PM   #4
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Quote:
Originally Posted by Denis View Post
n^4 - n^3 + n^2 - n = n*{n*[n*(n - 1) + 1] - 1}

Just got that...kinda accidentally...mean anything?
But that means you are squaring n by doing n*n!!

-Dan
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September 19th, 2018, 03:28 PM   #5
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Originally Posted by RichardJ View Post
Was there something else there that you saw or wondered about?
Don't lose any sleep Dick: was simply screwing around...
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September 19th, 2018, 04:15 PM   #6
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I'm not sure if this is just satirizing the other thread but this formula is actually quite useful. The RHS is how you would evaluate the polynomial, $n^4 - n^3 + n^2 - n$ using Horner's algorithm. If you haven't seen it before its pretty simple but very powerful.

https://en.wikipedia.org/wiki/Horner%27s_method
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September 19th, 2018, 06:28 PM   #7
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I knew that had a name - couldn't think of it though.
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