2013 Mock AIME I Problems/Problem 14

Problem

Let $$\begin{array}{r}P(x)=x^{2013}+4x^{2012}+9x^{2011}+16x^{2010}+\cdots +4052169x+4056196=\sum _{j=1}^{2014}{j}^2{x}^{2014-j}.\end{array}$$ If are its roots, then compute the remainder when is divided by 997.

Solution

Since 997 is prime, we have equals to mod 997, which by Vieta's equals -4. Thus our answer is 993 mod 997.