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Home » 8 of Wands: The Hidden Power Behind This Ancient Spell You Need to Master NOW! - High Altitude Science

8 of Wands: The Hidden Power Behind This Ancient Spell You Need to Master NOW! - High Altitude Science

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Thus, \( k = 5m + 2 \), so \( n = 10(5m + 2) + 4 = 50m + 24 \). The smallest positive \( n \) is \( n = 24 \). Check: \( 24^2 = 576 \), ends in 76 — valid.

📌 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 \( n = 26 \). Check: \( 26^2 = 676 \), ends in 76 — valid.

📌 Between 24 and 26, the smaller is 24. Therefore, the smallest positive integer whose square ends in 76 is \( \boxed{24} \).

📌 Question:** What is the remainder when the sum \( 1^3 + 2^3 + 3^3 + \dots + 12^3 \) is divided by 9?

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