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Time for first part = 120 / 60 = 2 hours - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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n \equiv 1 \pmod{7} \quad \text{and} \quad n \equiv 1 \pmod{11}
This implies:
n - 1 \equiv 0 \pmod{7} \quad \text{and} \quad n - 1 \equiv 0 \pmod{11...
So $ n - 1 $ is a common multiple of 7 and 11. Since 7 and 11 are copr...
\text{lcm}(7, 11) = 7 \cdot 11 = 77
Thus, $ n - 1 = 77k $ for some integer $ k $, and:
n = 77k + 1
We are to find the smallest such $ n > 50 $. Try $ k = 1 $:
n = 77 \cdot 1 + 1 = 78
Since $ 78 > 50 $, this is valid.

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