MathDB

Mediterranean M.C. 2010 Problem 4

Source:

July 12, 2010

modular arithmeticalgebrapolynomiallinear algebramatrixcombinatorics proposedcombinatorics

Problem Statement

Let

p

be a positive integer,

p>1.

Find the number of

m\times n

matrices with entries in the set

\left\{ 1,2,\dots,p\right\}

and such that the sum of elements on each row and each column is not divisible by

p.