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Jan 28th, 2002, 08:58 PM
#1
Thread Starter
Hyperactive Member
 Interesting stuff..
Playing with factorials I found the following
x^2 - x = x! (or) x(x-1) = x!
has unique Solution: x = 2
x^3 - 3x^2 + 2x = x! (or) x(x-1)(x-2) = x!
has unique Solution: x = 3
Similarly,
x^4 - 6x^3 + 11x^2 - 6x = x! has the unique solution x=4
and
x^5 - 10x^4 + 35x^3 - 50x^2 + 24x = x !
has the unique solution x=5
You can notice that solution for all these equation is the highest power of x in the equation. I think this is unique
because other than the equation x = 1 ...
I haven't heard of a polynomial equation that has a unique solution with the solution equal to the highest power of x in the equation.
The coefficents of these equation seems to follow a pattern.
I would like to know how to generate the coefficents for the nth degree equation.
The only cubic equation that can be equal to x! is
x^3 - 3x^2 + 2x
So... even the polynomial eqs are unique for a factorial.
Last edited by thinktank2; Jan 29th, 2002 at 12:09 AM.
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