MathDB
sum of products of numbers in rows and columns in 2x2 table is 2021

Source: Czech-Polish-Slovak Match Junior 2021, individual p1 CPSJ

September 12, 2021
number theory

Problem Statement

You are given a 2×22 \times 2 array with a positive integer in each field. If we add the product of the numbers in the first column, the product of the numbers in the second column, the product of the numbers in the first row and the product of the numbers in the second row, we get 20212021. a) Find possible values for the sum of the four numbers in the table. b) Find the number of distinct arrays that satisfy the given conditions that contain four pairwise distinct numbers in arrays.