Problem

Source: 2009 Cuba MO 1.3

Tags: combinatorics



In each square of an $n \times n$ board with $n\ge 2$, an integer is written not null. Said board is called Inca if for each square, the number written on it is equal to the difference of the numbers written on two of its neighboring squares (with a common side). For what values of $n$, can you get Inca boards ?