Let
N=3×5×7×11×13.
There are X possibilities for the units digit of a perfect square when it is represented in base N. Compute the last three digits of X (in base 10).
Details and Assumptions:
- We are talking about 3,5,7,11,13 in their decimal representations.
- You might want to use the fact that 3,5,7,11,13 are all primes.