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Home » Unlock Your Inner Artist: Top iPad Art Apps That Guarantee Stunning Masterpieces! - RTA

Unlock Your Inner Artist: Top iPad Art Apps That Guarantee Stunning Masterpieces! - RTA

📅 May 11, 2026 👤 scraface

May 11, 2026

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📌 الحل: لنأخذ أي أربعة أعداد صحيحة متتالية: $n, n+1, n+2, n+3$.

📌 يوجد على الأقل عددان زوجيان، وأحدهما قابل للقسمة على $4$، لذا يكون حاصل الضرب قابلاً للقسمة على $2^3 = 8$.

📌 يوجد على الأقل عدد قابل للقسمة على $3$.

📌 لذلك، يكون حاصل الضرب قابلاً للقسمة على $8 \cdot 3 = 24$.

📌 نختبر مثالاً: $1 \cdot 2 \cdot 3 \cdot 4 = 24$، والذي ليس قابلاً للقسمة على $48$.

📌 إذن، أكبر عدد صحيح يجب أن يقسم حاصل ضرب أي أربعة أعداد صحيحة متتالية هو $\boxed{24}$.

📌 السؤال: ما هي أكبر قيمة ممكنة للقاسم المشترك الأكبر $(a,b)$، إذا كان مجموع عددين صحيحين موجبين $a + b = 96$؟

📌 الحل: ليكن $d = \gcd(a, b)$. إذن $a = dx$، $b = dy$، حيث $\gcd(x, y) = 1$.

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