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You Won’t Believe Which Paramount Movies Are Dominating Box Office Now! - American Beagle Club

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 k \leq \left\lfloor \frac{97}{7} \right\rfloor = 13

📌 Therefore, \( k \) can range from 0 to 13. The number of integers \( k \) can take is:

📌 - 0 + 1 = 14

📌 Thus, there are 14 integers among the first 100 positive integers that are congruent to 3 modulo 7. Therefore, the final answer is:

📌 \boxed{14}

📌 What is the largest integer that must divide the product of any three consecutive integers?

📌 Consider three consecutive integers denoted as \( n, n+1, n+2 \).

📌 Among any three consecutive integers, one must be divisible by 2 (since every second integer is even).

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