Question 67
1. Let $p$ be an odd prime number.
a. Show that $p$ divides $n \cdot 2^{n} + 1$ for infinitely many positive integers $n$.
b. Find all $n$ satisfying the condition above when $p = 3$.
a. Show that $p$ divides $n \cdot 2^{n} + 1$ for infinitely many positive integers $n$.
b. Find all $n$ satisfying the condition above when $p = 3$.