Question 25
(GBR 2) Let $a,b,x,y$ be positive integers such that $a$ and $b$ have no common divisor greater than $1$. Prove that the largest number not expressible in the form $ax+by$ is $ab-a-b$. If $N(k)$ is the largest number not expressible in the form $ax+by$ in only $k$ ways, find $N(k)$.