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Home » Rounded to the nearest whole number: 93 km/h. - Carbonext

Rounded to the nearest whole number: <>93 km/h. - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Dividing by 7:

📌 -\frac{2}{7} \leq k \leq \frac{97}{7} \approx 13.857

📌 Since $ k $ must be a non-negative integer, valid values are $ k = 0, 1, 2, ..., 13 $, which gives 14 values.

📌 Thus, there are $ \boxed{14} $ integers between 1 and 100 that are congruent to 3 modulo 7.

📌 Question: What is the smallest positive integer $ n $ such that $ n^2 \equiv 1 \pmod{12} $?

📌 Solution: We are to find the smallest positive integer $ n $ such that:

📌 n^2 \equiv 1 \pmod{12}

📌 This implies $ n^2 - 1 \equiv 0 \pmod{12} $, or $ (n - 1)(n + 1) \equiv 0 \pmod{12} $.

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