Question 140
Let $p$ be an odd prime number, $h \lt p$ an integer, $e \in \{1,2\}$. We set $n = h \cdot p^{e} + 1$ and assume that: $$
\left\{\begin{array}{r}
n \mid 2^{n-1} - 1 \\
n \nmid 2^{h} - 1
\end{array}\right.
$$ Show that $n$ is first.
\left\{\begin{array}{r}
n \mid 2^{n-1} - 1 \\
n \nmid 2^{h} - 1
\end{array}\right.
$$ Show that $n$ is first.