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$y = \pm1$: $25x^2 = 144 + 3600 = 3744$, $x^2 = 3744/25 = 149.76$, 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:
$2^3$ (from 8),
$3^2$ (from 9),
$11$.