Problem

Source: Romania JBMO TST 2024 Day 2 P1

Tags: combinatorics, table



The integers from 1 to 49 are written in a $7\times 7$ table, such that for any $k\in\{1,2,\ldots,7\}$ the product of the numbers in the $k$-th row equals the product of the numbers in the $(8-k)$-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