Problem 1843

(a) Let $n = 8$. Determine whether there exists a labelling of an $8 \times 8$ grid such that the following condition is fulfilled: The difference of any two transversal products is always divisible by $65$.

(b) Let $n = 10$. Determine whether there exists a labelling of a $10 \times 10$ grid such that the following condition is fulfilled: The difference of any two transversal products is always divisible by $101$.