Problem of the Week 1196

Find Minus Two

Start with the set S = {0, 2014}. Then, repeatedly, expand S as follows.

Place into S any integer that is a root of a polynomial the coefficients of whichare in S.

Prove that the negative number −2 eventually appears in S.

Source: Baltic Way Mathematical Olympiad, 1996, Problem 12. Also, MAA NCS contest, 2014, Problem 9.

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