Question 2
A two-digit number $n$ is divided by the sum of its digits, giving remainder $r$.
a. Find a number $n$ such that $r=0$.
b. Show that $r$ cannot exceed $15$.
c. Show that for every remainder $r$ at most $12$, there is a number $n$ that leaves remainder $r$ when divided by its digit sum.
a. Find a number $n$ such that $r=0$.
b. Show that $r$ cannot exceed $15$.
c. Show that for every remainder $r$ at most $12$, there is a number $n$ that leaves remainder $r$ when divided by its digit sum.