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 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 .
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.