Binomials and Powers
Problem 830
Let $\displaystyle S(n)=\sum\limits_{k=0}^{n}\binom{n}{k}k^n$.
You are given, $S(10)=142469423360$.
Find $S(10^{18})$. Submit your answer modulo $83^3 89^3 97^3$.
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Let $\displaystyle S(n)=\sum\limits_{k=0}^{n}\binom{n}{k}k^n$.
You are given, $S(10)=142469423360$.
Find $S(10^{18})$. Submit your answer modulo $83^3 89^3 97^3$.