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Home » You Won’t Believe What Motobuki Can Do—Trailblazing Upgrades Inside! - 500apps

You Won’t Believe What Motobuki Can Do—Trailblazing Upgrades Inside! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📝 Recent Posts

Equality occurs when $ a = b = c = rac{1}{3} $. Thus, the minimum val...
Question: Let $ h(x) $ be a polynomial such that $ h(x^3 + 1) = x^6 +...
Solution: Observe that the right-hand side is $ (x^3 + 1)^2 + 2 $. How...
h(x^3 + 1) = (x^3 + 1)^2 + 2 \Rightarrow h(u) = u^2 + 2
Then, substitute $ u = x^3 - 1 $:
h(x^3 - 1) = (x^3 - 1)^2 + 2 = x^6 - 2x^3 + 1 + 2 = x^6 - 2x^3 + 3
oxed{x^6 - 2x^3 + 3}
Question: Find the remainder when $ (x^2 + x + 1)^3 $ is divided by $...
Solution: Let us compute $ (x^2 + x + 1)^3 \mod (x^2 - x + 1) $.
Note that $ x^2 + x + 1 $ and $ x^2 - x + 1 $ are related via complex...

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