Question 2
Let $n\gt 1$ be an integer not divisible by $1997$. Put
$$a_m=m+\frac{mn}{1997}\quad(m=1,2,\ldots,1996),$$
$$b_m=m+\frac{1997m}{n}\quad(m=1,2,\ldots,n-1).$$
Arrange all the numbers $a_i,b_j$ in increasing order. Prove that the difference between any two consecutive terms is less than $2$.
$$a_m=m+\frac{mn}{1997}\quad(m=1,2,\ldots,1996),$$
$$b_m=m+\frac{1997m}{n}\quad(m=1,2,\ldots,n-1).$$
Arrange all the numbers $a_i,b_j$ in increasing order. Prove that the difference between any two consecutive terms is less than $2$.