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Home » You Won’t Believe How Powerful Umbreon + Espeon Team Mixes Streak battles! - DNSFLEX

You Won’t Believe How Powerful Umbreon + Espeon Team Mixes Streak battles! - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 2Frage: Was ist die größte ganze Zahl, die das Produkt von drei aufeinanderfolgenden positiven ganzen Zahlen stets teilt?

📌 Lösung: Sei die drei aufeinanderfolgenden positiven ganzen Zahlen \( n, n+1, n+2 \). Unter drei aufeinanderfolgenden ganzen Zahlen ist immer eine durch 2 teilbar und mindestens eine durch 3 teilbar. Da dies für jedes \( n \) gilt, muss das Produkt \( n(n+1)(n+2) \) durch \( 2 \times 3 = 6 \) teilbar sein. Um zu prüfen, ob eine größere feste Zahl immer teilt: Betrachten wir \( n = 1 \): \( 1 \cdot 2 \cdot 3 = 6 \), teilbar nur durch 6. Für \( n = 2 \): \( 2 \cdot 3 \cdot 4 = 24 \), teilbar durch 6, aber nicht notwendigerweise durch eine höhere Zahl wie 12 für alle \( n \). Da 6 die höchste Zahl ist, die in allen solchen Produkten vorkommt, ist die größte ganze Zahl, die das Produkt von drei aufeinanderfolgenden positiven ganzen Zahlen stets teilt, \( \boxed{6} \).

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