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Home » 4x^2 - 9y^2 = (2x - 3y)(2x + 3y) - Red Crowns

4x^2 - 9y^2 = (2x - 3y)(2x + 3y) - Red Crowns

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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Solution:** The sequence 3, 9, 15, 21, ... is arithmetic with first te...
The \( n \)-th term is:
a_n = 3 + (n - 1) \cdot 6 = 6n - 3
We want the largest \( n \) such that \( a_n \leq 500 \):
6n - 3 \leq 500
\Rightarrow 6n \leq 503
\Rightarrow n \leq \frac{503}{6} \approx 83.83
So the largest integer \( n \) is 83.
Thus, there are 83 stable molecular points in the first 500 cubic unit...
\boxed{83}

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