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6^1 = 6 \Rightarrow 3 \cdot 6 = 18
6^0 = 1 \Rightarrow 2 \cdot 1 = 2
+ 144 = 1224, \quad 1224 + 18 = 1242, \quad 1242 + 2 = 1244
So, the base-ten equivalent is:
oxed{1244}
Question:** Find the smallest positive integer \(n\) such that \(n^3\) ends in the digits \(888\).
We seek the smallest \(n > 0\) such that:
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