A Problem of Divisibility
Arrange n×m digits aij (i = 1, ..., n; j = 1, ..., m) in a rectangular array. If read left to right, every row then represents a decimal integer, and so does every column if read from top downwards. In all, there are
Here's a problem. Assume it's known that all n + m numbers in the matrix but one are divisible by p. Prove that the remaining number is bound to be divisible by p as well.
The applet below helps you verify that this is so. All digits are clickable so that you can modify the matrix to your liking.
|What if applet does not run?|