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set of m x n matrices with entries in the set {0,1,2,3,4}

Source: Romania BMO TST 1989 p1

February 17, 2020
combinatoricsSumnumber theory

Problem Statement

Let MM denote the set of m×nm\times n matrices with entries in the set {0,1,2,3,4}\{0,1,2,3,4\} such that in each row and each column the sum of elements is divisible by 55. Find the cardinality of set MM.
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