38th Austrian Mathematical Competition 2007
Source: round2 problem1 - 2007x2007 table
February 7, 2009
quadraticsnumber theory unsolvednumber theory
Problem Statement
In a quadratic table with rows and columns is an odd number written in each field.
For is the sum of the numbers in the -th row and for is the sum of the numbers in the -th column.
is the product of all and the product of all .
Show that A\plus{}B\neq0