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Home » You Won’t Believe What Happens When a Teeter Totter Tumbles—Shocking Trial!, - Dachbleche24

You Won’t Believe What Happens When a Teeter Totter Tumbles—Shocking Trial!, - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 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

📌 \(888 \equiv 0 \pmod{8}\), so:

📌 n^3 \equiv 0 \pmod{8} \Rightarrow n \equiv 0 \pmod{2}

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