MathDB

4. Suppose that

\overline{A2021B}

is a six-digit integer divisible by

9

. Find the maximum possible value of

A \cdot B

.
5. In an arbitrary triangle, two distinct segments are drawn from each vertex to the opposite side. What is the minimum possible number of intersection points between these segments?
6. Suppose that

a

and

b

are positive integers such that

\frac{a}{b-20}

and

\frac{b+21}{a}

are positive integers. Find the maximum possible value of

a + b

Problem Statement