Question 17
A positive integer $n$ is said to be *good* if there exist positive integers $a$ and $b$ such that $a+b=n$ and $ab$ is divisible by $n$. For instance, $9$ is good since $3+6=9$ and $3 \times 6$ is divisible by $9$. Furthermore, $n$ is said to be *very good* if we can choose $a$ and $b$ to be distinct. Hence $9$ is very good.
a. Given that $2003$ is a prime, show that $2003$ is not good.
b. Is $2002$ good?
c. Find all positive integers which are good but not very good. Justify your answers.
a. Given that $2003$ is a prime, show that $2003$ is not good.
b. Is $2002$ good?
c. Find all positive integers which are good but not very good. Justify your answers.