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lyrics to my wish for you rascal flatts - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 This means $ n = 7k + 3 $ for some integer $ k $.

📌 We want $ 1 \leq 7k + 3 \leq 100 $.

📌 Subtracting 3 from all parts:

📌 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} $?

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