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📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 $y = 0$: $25x^2 = 3600 \Rightarrow x^2 = 144$, $x = \pm 12$.

📌 $y = \pm1$: $25x^2 = 144 + 3600 = 3744$, $x^2 = 3744/25 = 149.76$, not integer.

📌 $y = \pm5$: $25x^2 = 144(25) + 3600 = 3600 + 3600 = 7200$, $x^2 = 288$, not square.

📌 Eventually, only solutions are $(\pm12, 0)$.

📌 Thus, exactly 2 lattice points.

📌 Question: A high-performance computing simulation requires a grid size that is divisible by the least common multiple of all integers from 1 to 12. What is the smallest such grid size greater than 1 million?

📌 Solution: We seek the smallest multiple of $\mathrm{lcm}(1,2,\dots,12)$ greater than 1,000,000.

📌 Factor each number from 1 to 12:

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