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Home » Let height \( h \), then length \( l = 2h \), width \( w = h + 3 \). - SUpost

Let height \( h \), then length \( l = 2h \), width \( w = h + 3 \). - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 In a study of ancient bird nesting sites, a zoologist models population cycles using a number \( N \) such that \( N \equiv 3 \pmod{4} \), \( N \equiv 2 \pmod{5} \), and \( N \equiv 4 \pmod{7} \). What is the smallest positive \( N \) satisfying all three conditions?

📌 We solve the system of congruences:

📌 N \equiv 3 \pmod{4} \\

📌 N \equiv 2 \pmod{5} \\

📌 N \equiv 4 \pmod{7}

📌 Start with the first two:

📌 Step 1: Solve \( N \equiv 3 \pmod{4} \) and \( N \equiv 2 \pmod{5} \)

📌 Let \( N = 4a + 3 \). Substitute into second:

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