# Problem 479: Roots on the Rise
Let ak, bk, and ck represent the three solutions (real or complex
numbers) to the expression 1/x = (k/x)2(k+x2) - kx. For instance, for k
= 5, we see that {a5, b5, c5} is approximately {5.727244,
-0.363622+2.057397i, -0.363622-2.057397i}. Let S(n) = Σ
(ak+bk)p(bk+ck)p(ck+ak)p for all integers p, k such that 1 ≤ p, k ≤ n.
Interestingly, S(n) is always an integer. For example, S(4) = 51160.
Find S(106) modulo 1 000 000 007.