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38th Austrian Mathematical Competition 2007

Source: round2 problem1 - 2007x2007 table

February 7, 2009
quadraticsnumber theory unsolvednumber theory

Problem Statement

In a quadratic table with 2007 2007 rows and 2007 2007 columns is an odd number written in each field. For 1i2007 1\leq i\leq2007 is Zi Z_i the sum of the numbers in the i i-th row and for 1j2007 1\leq j\leq2007 is Sj S_j the sum of the numbers in the j j-th column. A A is the product of all Zi Z_i and B B the product of all Sj S_j. Show that A\plus{}B\neq0