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Home » Correction: Assume typo; try with Sₙ = 98 → n = 7. But original says 110. - Veritas Home Health

Correction: Assume typo; try with Sₙ = 98 → n = 7. But original says 110. - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 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 حاص...
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 للقسم...
إذن، أكبر عدد صحيح يجب أن يقسم حاصل ضرب أي أربعة أعداد صحيحة متتالية ه...
السؤال: ما هي أكبر قيمة ممكنة للقاسم المشترك الأكبر $(a,b)$، إذا كان م...
الحل: ليكن $d = \gcd(a, b)$. إذن $a = dx$، $b = dy$، حيث $\gcd(x, y) =...
ثم $a + b = d(x + y) = 96$، لذا يجب أن يكون $d$ قاسمًا للعدد $96$.
لتعظيم $d$، نختار أكبر قاسم للعدد $96$ بحيث يكون $x + y$ عددًا صحيحًا...

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