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purdue boilermakers football vs michigan wolverines football stats - IQnection

📅 May 5, 2026 👤 scraface

May 05, 2026

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Question: How many of the 100 smallest positive integers are congruent...
Solution: We seek the number of positive integers $n \leq 100$ such th...
Such numbers form an arithmetic sequence: $3, 10, 17, \dots$, with fir...
The general term is:
n_k = 3 + (k-1)\cdot 7 = 7k - 4.
We require $n_k \leq 100$:
7k - 4 \leq 100 \Rightarrow 7k \leq 104 \Rightarrow k \leq rac{104}{7...
So the largest integer $k$ is $14$.
Thus, there are $14$ such numbers.
Check: $n_{14} = 7(14) - 4 = 98 - 4 = 94 \leq 100$, and $n_{15} = 7(15...

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