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Home » So $2^9 \equiv 12 \pmod25$. - AMAZONAWS

So $2^9 \equiv 12 \pmod25$. - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 e 0 \) and \( z, w \in \mathbb{C} \).

📌 Solution:** Let \( u = rac{z + w}{z - w} \), so the second term is \( rac{1}{u} \), and the equation becomes:

📌 u + rac{1}{u} = 2.

📌 Multiply by \(u\): \( u^2 - 2u + 1 = 0 \Rightarrow (u - 1)^2 = 0 \Rightarrow u = 1 \).

📌 rac{z + w}{z - w} = 1 \Rightarrow z + w = z - w \Rightarrow 2w = 0 \Rightarrow w = 0.

📌 But this contradicts \( w

📌 Wait â unless the equation allows limit behavior, but we must re-express carefully.

📌 Actually, \( u + rac{1}{u} = 2 \) implies \( u = 1 \) (since for complex \(u\), this only holds if \(|u| = 1\) and conjugate symmetry, but equality to 2 forces \(u = 1\) in \( \mathbb{C} \) only if real and positive, but let's solve generally).

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