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 which are in S.
Prove that the negative number −2 eventually appears in S.
Construct the equation 2014x + 2014 = 0.
Then x=-1 is added to S.
Construct (-1)*x + 2014 = 0.
Then x=-2014 is added to S.
Construct 2014x + (-2014) = 0
Then x=1 is added to S.
2014 in binary is 11111011110. Construct 1*x^10 + 1*x^9 + 1*x^8 + 1*x^7 + 1*x^6 + 1*x^4 + 1*x^3 + 1*x^2 + 1*x + (-2014) = 0.
Then x=2 is added to S.
Finally, construct x + 2 = 0.
Then x=-2 is added to S.
How to add -2
