MathDB

High school graduate Igor Petrov, who dreamed of becoming a diplomat, took the entrance exam in mathematics to Moscow University. Igor remembered all the problems offered during the exam, but forgot some numerical data in one. This is the task:
“When multiplying two natural numbers, the difference of which is

10

, an error was made: the hundreds digit in the product was increased by

2

. When dividing the resulting (incorrect) product by the smaller of the factors, the result was quotient

k

and remainder

r

.. Find the numbers that needed to be multiplied.” .
The values of

k

and

r

were given in the condition, but Igor forgot them. However, he remembered that the problem had two answers. What could the numbers

k

and

r

be equal to (they are both integers and positive)?
Note. The problem in question was proposed at one of the humanities faculties of Moscow State University in 1991.

Problem Statement