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Home » For the prime 2: the highest power is \(2^3\). - Dachbleche24

For the prime 2: the highest power is \(2^3\). - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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Thus, \( k = 5m + 2 \), so \( n = 10(5m + 2) + 4 = 50m + 24 \). The sm...
Now consider \( n \equiv 6 \pmod{10} \): \( n = 10k + 6 \).
n^2 = 100k^2 + 120k + 36 \equiv 20k + 36 \pmod{100}
Set \( 20k + 36 \equiv 76 \pmod{100} \):
20k \equiv 40 \pmod{100} \implies k \equiv 2 \pmod{5}
So \( k = 5m + 2 \), \( n = 10(5m + 2) + 6 = 50m + 26 \). Smallest \(...
Between 24 and 26, the smaller is 24. Therefore, the smallest positive...
Question:** What is the remainder when the sum \( 1^3 + 2^3 + 3^3 + \d...
For \( n = 12 \):
\sum_{k=1}^{12} k^3 = \left( \frac{12 \cdot 13}{2} \right)^2 = (78)^2...

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