MathNet 2015-part-07 — 185 problems (EN–VI) Question 138

Let $N$ be the number of functions $f$ from $\{1,2, \ldots, 101\} \rightarrow \{1,2, \ldots, 101\}$ such that $f^{101}(1)=2$. Find the remainder when $N$ is divided by 103.