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How would I code the solution to this problem? Let P be a polynomial satisfying P(x + 1) + P(x − 1) = x^3

for all real numbers x. I am trying to find P(x)

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  • $\begingroup$ I am trying to find P(x) $\endgroup$ – Bob Jones Mar 23 '19 at 15:44
  • $\begingroup$ Please edit your question to include all relevant info. Also, what have your tried, and where are you stuck? $\endgroup$ – corey979 Mar 23 '19 at 15:45
  • $\begingroup$ Well, I am not really experienced in using Mathematica but I tried using solve but that did not work. $\endgroup$ – Bob Jones Mar 23 '19 at 15:47
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    $\begingroup$ This does it: FullSimplify[RSolve[P[x + 1] + P[x - 1] == x^3, P[x], x], x \[Element] Reals]. You can set the arbitrary constants C[1] and C[2] to zero to get a real polynomial. $\endgroup$ – corey979 Mar 23 '19 at 15:52

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