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Home » \[ S_n-1 = 3(n-1)^2 + 5(n-1) \] - Abu Waleed Tea

\[ S_n-1 = 3(n-1)^2 + 5(n-1) \] - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 We solve for $ k $: find the modular inverse of 7 modulo 13.

📌 $ 7 \cdot 1 = 7

📌 $ 7 \cdot 2 = 14 \equiv 1 \pmod{13} $

📌 So $ 7^{-1} \equiv 2 \pmod{13} $

📌 k \equiv 2 \pmod{13} \Rightarrow k = 13m + 2

📌 Then $ L = 7k = 7(13m + 2) = 91m + 14 $

📌 For $ m = 0 $, $ L = 14 $ (two-digit)

📌 Check: Is 14 $ \equiv 1 \pmod{13} $?

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