# Problem 402: Integer-valued polynomials
It can be shown that the polynomial n4 + 4n3 + 2n2 + 5n is a multiple of
6 for every integer n. It can also be shown that 6 is the largest
integer satisfying this property. Define M(a, b, c) as the maximum m
such that n4 + an3 + bn2 + cn is a multiple of m for all integers n. For
example, M(4, 2, 5) = 6. Also, define S(N) as the sum of M(a, b, c) for
all 0 < a, b, c ≤ N. We can verify that S(10) = 1972 and S(10000) =
2024258331114. Let Fk be the Fibonacci sequence: F0 = 0, F1 = 1 and Fk =
Fk-1 + Fk-2 for k ≥ 2. Find the last 9 digits of Σ S(Fk) for 2 ≤ k ≤
1234567890123.