In Example 3.1 of the book/lecture, it was noted that:

• 72 has 12 factors, an even number of factors.
• 36 has 9 factors, an odd number of factors.

In fact, any number that IS a perfect square has an odd number of factors. Any number that IS NOT a perfect square has an even number of factors.

Problem 3.21 is asking you to explain why this is always true (prove the statements). Why do perfect squares have an odd number of factors? Why do all other numbers have an even number of factors.

There are different ways of approaching this, but one easy way is thinking about pairing up the factors.