If f(n) = 2^x * 3^y * 5^z for a three-digit number n, what happens if f(m) = 9 * f(v) where m and v are also three-digit numbers?

To determine the significance of the given condition f(m) = 9 * f(v) in the context of the function f(n) = 2^x * 3^y * 5^z, let's first break down what is indicated by f(m) and f(v).

Here, f(n) expresses a three-digit number in terms of its prime factorization, specifically focusing on the prime bases 2, 3, and 5. The statement f(m) = 9 * f(v) implies a relationship between the numbers m and v where f(m) is nine times the value of f(v). In terms of prime factorization, we can express 9 as 3^2. Hence, this means:

f(m) = 3^2 * f(v)

This tells us that the contribution from the factor 3 in the prime factorization of the three-digit number m must be exactly 2 more than that of v.

Now we can rewrite f(m) in terms of f(v):

f(m) = 2^x * 3^(y + 2) * 5^z

This indicates that if f(m) is derived from f(v) by multiplying the contribution of