MathDB

Find all pairs of natural numbers

(n, k)

with the following property: Given a

k\times k

array of cells, such that every cell contains one integer, there always exists a path from the left to the right edges such that the sum of the numbers on the path is a multiple of

n

.
Note: A path from the left to the right edge is a sequence of cells of the array

a_1, a_2, ... , a_m

so that

a_1

is a cell of the leftmost column,

a_m

is the cell of the rightmost column, and

a_{i}

a_{i+1}

share an edge for all

i = 1, 2, ... , m -1

Problem Statement