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caesar in war for the planet of the apes - AssociationVoting

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 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 $n_{15} = 7(15) - 4 = 105 - 4 = 101 > 100$.

📌 So only $14$ terms.

📌 Therefore, the number is $oxed{14}$.

📌 Question: What is the remainder when the sum $1^3 + 2^3 + 3^3 + \dots + 10^3$ is divided by $9$?

📌 Solution: Use the formula for the sum of cubes:

📌 \left(\sum_{k=1}^{n} k^3

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