Thursday, 29 January 2026

Exercise (4.5).5

Prove that a prime number is a deficient number.


A number $n$ is deficient if the sum of its proper factors is less than $n$.

A prime number $p$ has only two factors, 1 and $p$ itself. It has only one proper factor, 1.


And so any prime is deficient because the sum of its proper factors is always 1, which is less than any prime.