Tuesday, 28 October 2025

Exercise (2.1).13

The tau function $𝜏 (n)$ was defined in Chapter 1 as the number of positive factors of n. For example,

$𝜏 (12) = 6$ because 12 has factors 1, 2, 3, 4, 6, 12.

Show that for a prime number, $p$, we have $𝜏 (p) = 2$.


A prime $p$ has only 2 positive factors, 1 and $p$, and so the number is 2.

$$ \tau(p) = 2 $$