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Home » \frac70 \cdot 6638760 = \frac462038760 = \frac77646 - AIKO, infinite ways to autonomy.

\frac70 \cdot 6638760 = \frac462038760 = \frac77646 - AIKO, infinite ways to autonomy.

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Solution: We compute the sum modulo 8. First, reduce each term modulo 8:

📌 \equiv 7 \pmod{8}, \quad 11073 \equiv 1 \pmod{8}, \quad 11075 \equiv 3 \pmod{8}, \quad 11077 \equiv 5 \pmod{8}

📌 Now sum them modulo 8:

📌 + 1 + 3 + 5 = 16 \equiv 0 \pmod{8}

📌 Question: What two-digit positive integer is one more than a multiple of $ 7 $ and leaves a remainder of $ 3 $ when divided by $ 5 $?

📌 Solution: Let $ x $ be the two-digit number. We are given:

📌 x \equiv 1 \pmod{7}, \quad x \equiv 3 \pmod{5}

📌 We solve this system using the Chinese Remainder Theorem.

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