# Thanksgiving Challenge (NEW: Posted December 18, 2013)

**As Thanksgiving is rapidly approaching, many turkeys are understandably worried. Several of them have gotten together and convinced humanity to accept the following challenge (rather than settling things with the sword).**

**The turkeys will create a polynomial P(x) such that, no matter what integer k the humans give them, the output P(k) will be an integer. If they can do this with one of the coefficients of P(x) being 1/2013 then no turkeys will be eaten for the rest of 2013.**

**Can the turkeys succeed? More generally, if you give them finitely many years (say n+1 years) can they create a similar polynomial which has 1/2013, 1/2014, …, 1/(2013+n) as coefficients?**

Note: This was originally the November 2013 Conundrum at Williams College. Problem communicated by Mihai Stoiciu, phrasing by Steven Miller.

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