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Numbers in the table

Source: St Petersburg Olympiad 2014, Grade 9, P7

October 27, 2017
number theory

Problem Statement

Natural a,b,ca,b,c are pairwise prime. There is infinite table with one integer number in every cell. Sum of numbers in every a×aa \times a, every b×bb \times b, every c×cc \times c squares is even. Is it true, that every number in table must be even?
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