Project Euler Problem 812
A dynamical polynomial is a monicleading coefficient is 1 polynomial f(x) with integer coefficients such that f(x) divid
Solution
Answer: 986262698
Using the dynamical structure of $x^2-2$, the problem decomposes into independent dyadic chains indexed by odd parts. The counting function becomes a coefficient extraction from a generating function built from these chains, with one exceptional chain for odd part $1$. A dynamic programming coefficient extraction modulo $998244353$ reproduces the checkpoints:
- $S(2)=6$
- $S(5)=58$
- $S(20)=122087$
matching the problem statement. The computed value for $S(10000)$ is:
Answer: 818277002