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Home » This Easy Formula Will Calculate How Many Laps Equal a Mile Forever! - Baxtercollege

This Easy Formula Will Calculate How Many Laps Equal a Mile Forever! - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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oxed{1244}
Question:** Find the smallest positive integer \(n\) such that \(n^3\)...
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}...
Step 1: Solve modulo 8
\(888 \equiv 0 \pmod{8}\), so:
n^3 \equiv 0 \pmod{8} \Rightarrow n \equiv 0 \pmod{2}
In fact, since \(8 = 2^3\), for \(n^3 \equiv 0 \pmod{8}\), \(n\) must...
If \(n \equiv 0 \pmod{2}\), then \(n^3 \equiv 0 \pmod{8}\) only if \(n...

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