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predominantly killer clickbait-style question titles: - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 But working modulo $7$, we can compute the sum directly using cyclicity. First, find the pattern of $3^k \mod 7$:

📌 3^1 &\equiv 3 \mod 7 \\

📌 3^2 &\equiv 9 \equiv 2 \mod 7 \\

📌 3^3 &\equiv 3 \cdot 2 = 6 \mod 7 \\

📌 3^4 &\equiv 3 \cdot 6 = 18 \equiv 4 \mod 7 \\

📌 3^5 &\equiv 3 \cdot 4 = 12 \equiv 5 \mod 7 \\

📌 3^6 &\equiv 3 \cdot 5 = 15 \equiv 1 \mod 7 \\

📌 So the powers of $3 \mod 7$ repeat every 6 terms. The cycle length is $6$.

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