4

Part of 2010 Mediterranean Mathematics Olympiad

Problems(1)

Mediterranean M.C. 2010 Problem 4

Source:

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.

modular arithmeticalgebrapolynomiallinear algebramatrixcombinatorics proposedcombinatorics