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Home » Explore Long Lake Park MN’s New Brightside Magic—ncrinism Site Unveiled! - Leaselab

Explore Long Lake Park MN’s New Brightside Magic—ncrinism Site Unveiled! - Leaselab

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 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 $:

📌 \sum_{k=1}^{10} k^3 = \left( \frac{10 \cdot 11}{2} \right)^2 = (55)^2 = 3025

📌 Now compute $ 3025 \mod 7 $. First, reduce 55 modulo 7:

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