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How to divide a big number into small numbers?
Sorry in advance for the title. I didn't know how to put my problem in a short question. I have this problem: "Dividing a big number into small numbers." I'm thinking of an arbitrary big number. In this number we could have negative numbers. I have been trying to calculate this for a while and I have gotten this result:
$U(N)=4 N^4-15 N^3+32 N^2-24 N+4$
$V(N)=3 N^4-15 N^3+22 N^2-24 N+4$
These functions are both where N = total number of numbers we want, but their value changes because I try different values:
$U(5) = -2$
$V(5) = 2$
How do I get these values?
A:
It looks like you're just computing the coefficients of $N^4$, $N^3$, and $N^2$. In fact, this is correct since the general formula for the $m$th power of a polynomial is the form $a_mN^m+a_{m-1}N^{m-1}+\cdots+a_0$. For the power in question, that gives
$
U(N) = 4(a_4N^4+a_3N^3+a_2N^2+a_1N+a_0) - 15(a_4N^4+a_3N^3+a_2N^2+a_1N+a_0) + \cdots = \cdots = N\left(4(a_4-15a_0)+3(4a_3-15a_2)+2(4a_2-15a_1)\right).
$
So if you want the value of $U(N)$ for $N = 5$, that tells you the coefficients of $N^5 0b46394aab
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