Detailed Instructions: Given a math problem with context and a question and 5 answer choices, the task is to provide the correct answer choice based on the problem. You must choose one of the given answer choices by letter: a, b, c, d, or e; anything else is invalid.
Q: Problem: a = 5 ^ 10 - 625 ^ 2 and a / x is an integer, where x is a positive integer greater than 1, such that it does not have a factor p such that 1 < p < x, then how many different values for x are possible ?
Options: a. none, b. one, c. two, d. three, e. four
A:
c