# Last Digits In Base 18815

Let $$X$$ be the number of distinct possibilities for the units digit of a perfect cube when written in base $$18815$$. Find the last three digits of $$X$$ (in decimal base).

Details and assumptions

• The prime factorization of $$18815$$ is $$18815= 5 \times 53 \times 71$$.

• We're talking about $$18815$$ in its decimal representation.

• This problem is similar to this one.

×