Problem

Source: Romania JBMO TST 2024 Day 2 P1

Tags: combinatorics, table



The integers from 1 to 49 are written in a 7×7 table, such that for any k{1,2,,7} the product of the numbers in the k-th row equals the product of the numbers in the (8k)-th row. Prove that there exists a row such that the sum of the numbers written on it is a prime number. Give an example of such a table. Cristi Săvescu