N \equiv 3 \pmod{4} \\
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- \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 2 \pmod{5} \\
- N \equiv 4 \pmod{7}
- Start with the first two:
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