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Home » New England Uncovered: The True Heart of America You Never Knew Existed! - Crankk.io

New England Uncovered: The True Heart of America You Never Knew Existed! - Crankk.io

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 \( k = 30 \): sum = \( 3+0 = 3 \), \( 30 \div 3 = 10 \), yes!

📌 So \( k = 30 \) is divisible by digit sum (3), and \( 30 \div 7 = 4 \times 7 + 2 \Rightarrow 30 \equiv 2 \pmod{7} \).

📌 Thus, the smallest such two-digit number is:

📌 \boxed{30}

📌 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} \\

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