Last Digits In Base 18815

Number Theory Level 5

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.


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