To determine which option is correct, we need to find the values of a and b that satisfy the given condition.

Let's start by expanding the given expression: 23n - bn - a.

- We can factor out n: n(23 - b) - a.

We are told that this expression is divisible by 49, so we can write it as:

n(23 - b) - a = 49k, where k is an integer.

To simplify the expression further, let's rearrange it:

n(23 - b) = a + 49k.

We know that 49 is a prime number, so it must divide either n or (23 - b). Let's consider both cases:

Case 1: 49 divides n
- If 49 divides n, then we can write n as 49m, where m is an integer.
- Substituting this into our expression, we get:
49m(23 - b) = a + 49k.
- Dividing both sides by 49, we have:
m(23 - b) = a/49 + k.
- Since m and (23 - b) are integers, the right side of the equation must also be an integer.
- This means a/49 must be an integer, which implies that a is a multiple of 49.
- The only option where a is a multiple of 49 is option B: (1, 7).

Case 2: 49 divides (23 - b)
- If 49 divides (23 - b), then we can write (23 - b) as 49m, where m is an integer.
- Substituting this into our expression, we get:
n(49m) = a + 49k.
- Dividing both sides by 49, we have:
n(7m) = a/49 + k.
- Since n and (7m) are integers, the right side of the equation must also be an integer.
- This means a/49 must be an integer, which implies that a is a multiple of 49.
- Again, the only option where a is a multiple of 49 is option B: (1, 7).

Therefore, the correct answer is option B: (1, 7).