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Home » Check for $3 \cdot 9 = 9$: yes. - Dyverse

Check for $3 \cdot 9 = 9$: yes. - Dyverse

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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

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