Thursday, 29 January 2026

Exercise (4.5).6

Show that the following is false:

‘An even number is an abundant number.’


We can show this with a counter-example.

Consider the even number 4. It has two proper factors, 1 and 2$. The sum is 3. which is less than 4, and so 4 is deficient, not abundant.

Another, even simpler example, is the even number 2, whose only proper factor is 1, and so the sum is 1, which is less than 2, leaving 2 as a deficient number.