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Home » Wait — perhaps three consecutive odd integers? But not specified. - Groen Casting

Wait — perhaps three consecutive odd integers? But not specified. - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 with equality when $ b = 1 $, i.e., $ y = z $.

📌 Thus, the minimum value of the entire expression is

📌 - \log(2).

📌 This value is achievable when $ x = y = z $, so the minimum is

📌 oxed{3 - \log 2}.

📌 Question: Find the remainder when $ (x^2 + 1)^{2025} + 1 $ is divided by $ x^4 + x^2 + 1 $.

📌 Let $ f(x) = (x^2 + 1)^{2025} + 1 $, and we are to find the remainder when $ f(x) $ is divided by $ x^4 + x^2 + 1 $.

📌 Let $ d(x) = x^4 + x^2 + 1 $. Note that

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