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Home » eq d_3 $: 2 â 12 - Portal da AcÃºstica

eq d_3 $: 2 â 12 - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 The product includes:

📌 At least one multiple of 3 → $ 3 $

📌 At least three factors of 2: among four consecutive numbers, the even numbers contribute at least $ 2 + 1 = 3 $ factors of 2 (e.g., 2 and 4 give $ 2^1 $ and $ 2^2 $).

📌 Additionally, among four consecutive numbers, one is divisible by 4, and another even → total $ 2^3 = 8 $

📌 Also, one is divisible by 4 and another even → but already included

📌 Moreover, in every set of 4 consecutive integers, one is divisible by 4, one by 2 (not divisible by 4), and one by 3 → so minimum $ 2^3 \cdot 3 = 24 $

📌 But test $ 1\cdot2\cdot3\cdot4 = 24 $ → divisible by 24

📌 $ 2\cdot3\cdot4\cdot5 = 120 $, divisible by 24

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