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Table with digits

Source: Moscow Math Olympiad 2017, Grade 11, P11

April 25, 2017
combinatoricsnumber theory

Problem Statement

There is one nonzero digit in every cell of 2017×20172017\times 2017 table. On the board we writes 40344034 numbers that are rows and columns of table. It is known, that 40334033 numbers are divisible by prime pp and last is not divisible by pp. Find all possible values of pp.
Example for 2×22\times2. If table is |1|4| |3|7|. Then numbers on board are 14,37,13,4714,37,13,47