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Home » Thus, the $ y $-intercept point is $ oxed(0, 1) $. - IQnection

Thus, the $ y $-intercept point is $ oxed(0, 1) $. - IQnection

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Question: A cyber-resilience consultant in Toronto is modeling secure key rotation intervals and observes that a system updates its encryption key every \( k \) hours, where \( k \) is the smallest positive integer such that \( k \equiv 3 \pmod{5} \), \( k \equiv 4 \pmod{7} \), and \( k \equiv 2 \pmod{9} \). What is the value of \( k \)?

📌 Solution: We solve the system of congruences:

📌 egin{cases}

📌 k \equiv 3 \pmod{5} \

📌 k \equiv 4 \pmod{7} \

📌 k \equiv 2 \pmod{9}

📌 We apply the Chinese Remainder Theorem step by step.

📌 First, solve the first two congruences:

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