I’ll start by stating the theorem. As we hit new topics, I will sidetrack, tackle those topics and than continue on.
We first must figure out how to 𝟇(𝒎). We will use a technique known as inclusion/exclusion. Namley, 𝟇(𝙥), where 𝙥 is a prime can be written
Example. Find 𝟇(4).
We can break 𝟇(4) into its prime factors ⇒ 𝟇(22). Since 2 is a prime, we can use our rule of
Which simplfies to,
Which evaluates to,