Which of the following options represents a pair of integers whose sum and difference are both zero? a) one b) zero c) two d) Cannot be determined

We are looking for a pair of integers $(a,b)$ such that their sum $a+b$ is zero AND their difference $a-b$ is zero.
We set up a system of equations:

1. $a+b=0$
2. $a-b=0$

Add equation (1) and equation (2):
$(a+b) + (a-b) = 0+0$
$2a = 0$
$a = 0$

Substitute $a=0$ into equation (1):
$0+b=0$
$b=0$

The pair of integers is $(0,0)$.
For this pair:
Sum: $a+b = 0+0 = 0$
Difference: $a-b = 0-0 = 0$

Both the sum and the difference are 0. Since 0 is an integer, this pair $(0,0)$ satisfies the condition that both their sum and difference result in zero.

Therefore, there is a pair of integers whose sum and difference both result in zero.

The final answer is $\boxed{\text{b) zero.}}$