Let n = 2^8 \cdot 3^9 \cdot 5^{10} \cdot 7^{11}. For k a positive integer, let f(k) be the number of integers 0 \leq x < n such that x^2 \equiv k^2 \pmod{n}. Compute the number of positive integers k such that k \mid f(k).
Let n = 2^8 \cdot 3^9 \cdot 5^{10} \cdot 7^{11}. For k a positive integer, let f(k) be the number of integers 0 \leq x < n such that x^2 \equiv k^2 \pmod{n}. Compute the number of positive integers k such that k \mid f(k).