January 26th, 2015, 03:51 PM  #1 
Member Joined: Jan 2015 From: Orlando, Florida Posts: 92 Thanks: 10  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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differences, finite 
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