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January 26th, 2015, 03:51 PM   #1
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Finite Differences

Let z be a complex number and k a positive integer such that z
k
is a positive real number other than
1. Let f(n) denote the real part of the complex number z
n. Assume the parabola p(n) = an^2 + bn + c
intersects f(n) four times, at n = 0, 1, 2, 3. Assuming the smallest possible value of k, find the largest
possible value of a.

The solution here: http://hmmt.mit.edu/static/archive/n...2014/theme.pdf
one part that mentions f(3) − 3f(2) + 3f(1) − f(0) = 0.
Can someone explain how to use finite differences on polynomials/other functions and what they do?
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