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when is the a&m game - Network4

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 We want $ a_k \leq 100 $, so:

📌 5k - 3 \leq 100 \Rightarrow 5k \leq 103 \Rightarrow k \leq \frac{103}{5} = 20.6

📌 Thus, $ k = 1, 2, \dots, 20 $, so there are 20 such numbers.

📌 Therefore, the number of integers is $ \boxed{20} $.

📌 Question: What is the remainder when the sum $ 1^3 + 2^3 + 3^3 + \dots + 10^3 $ is divided by 7?

📌 Solution: We use the formula for the sum of cubes:

📌 \sum_{k=1}^{n} k^3 = \left( \frac{n(n+1)}{2} \right)^2

📌 For $ n = 10 $:

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