We seek the smallest \(n > 0\) such that:
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- So, the base-ten equivalent is:
- oxed{1244}
- Question:** Find the smallest positive integer \(n\) such that \(n^3\) ends in the digits \(888\).
- n^3 \equiv 888 \pmod{1000}
- This means \(n^3 \equiv 888 \pmod{8}\) and \(n^3 \equiv 888 \pmod{125}\), since \(1000 = 8 imes 125\) and \(\gcd(8,125)=1\).
- Step 1: Solve modulo 8
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