Budstock Is Stocking Up on the Hottest Deals—Dont Miss Out Before Its Gone!

Budstock Is Stocking Up on the Hottest Deals—Dont Miss Out Before Its Gone!

Budstock Is Stocking Up on the Hottest Deals—Dont Miss Out Before Its Gone!

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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),$11$.