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Home » n^3 \equiv 888 \pmod1000 - Crankk.io

n^3 \equiv 888 \pmod1000 - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Set \( P'(x) = 0 \): no solution. So minimum does not exist — function decreases for large \( x \)? No, \( -0.5x \) dominates, so \( P(x) \to -\infty \), impossible.

📌 This suggests the model is invalid, but for math olympiad, likely the function is \( C(x) = 5000 + 120x + 0.5x^2 \). But it says \( -0.5x^2 \).

📌 Wait — perhaps it's \( C(x) = 5000 + 120x - 0.5x^2 \), but \( x \) has an upper limit. But no.

📌 Alternatively, the term \( -0.5x^2 \) may be a typo, and it should be \( +0.5x^2 \). Let's assume that, as it's common in real models.

📌 So assume \( C(x) = 5000 + 120x + 0.5x^2 \). Then average cost:

📌 P(x) = \frac{5000}{x} + 120 + 0.5x

📌 Now take derivative:

📌 P'(x) = -\frac{5000}{x^2} + 0.5

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