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Home » Second derivative: \(f''(x) = 18x - 4\) - Fine VPN

Second derivative: \(f''(x) = 18x - 4\) - Fine VPN

📅 May 13, 2026 👤 scraface

May 13, 2026

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📌 This implies $ n^2 - 1 \equiv 0 \pmod{12} $, or $ (n - 1)(n + 1) \equiv 0 \pmod{12} $.

📌 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.

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