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Home » Final Clarified Question (if LCM allowed): - ECD Germany

Final Clarified Question (if LCM allowed): - ECD Germany

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 So $ 12 \mid (n - 1)(n + 1) $.

📌 We test small values of $ n $:

📌 $ n = 1 $: $ 1^2 = 1 \equiv 1 \pmod{12} $ ✅

📌 Thus, the smallest such $ n $ is $ \boxed{1} $.

📌 Solution: Consider four consecutive integers: $ n, n+1, n+2, n+3 $.

📌 The product is $ P = n(n+1)(n+2)(n+3) $.

📌 Among any four consecutive integers, one is divisible by 4.

📌 At least two are even, so the product is divisible by $ 2^3 = 8 $.

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