Any member of is of the form (a, b) where a is in , b is in and multiplication is coordinate wise. That is, to be a zero divisor we must have for n and m integers. Since p is prime, at least one of a or c is a multiple of p and so is congruent to 0 modulo p. Either one of b or d is a multiple of , and so congruent to 0 modulo or both b and d are multiples of p.