Question 29
Let $\phi(n)$ denote the number of positive integers less than or equal to a given integer $n$ that are relatively prime to $n$. For example, $\phi(6) = |\{1, 5\}| = 2$ and $\phi(1) = |\{1\}| = 1$.
Let $a, b, c, d$ be nonnegative integers such that $\phi(2^a(2b+1)) = 2^c(2d+1)$. If $b \ge 1$ then show that
(1) $a \le c$ and,
(2) $b \ge 2d + 1$.
Let $a, b, c, d$ be nonnegative integers such that $\phi(2^a(2b+1)) = 2^c(2d+1)$. If $b \ge 1$ then show that
(1) $a \le c$ and,
(2) $b \ge 2d + 1$.