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📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 $$Question: How many of the 100 smallest positive integers are congruent to 3 modulo 7?

📌 Solution: We are asked to count how many of the first 100 positive integers satisfy the congruence:

📌 n \equiv 3 \pmod{7}

📌 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:

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