Do there exist positive integers $A, B, C$ such that all seven numbers $$A, B, C, A+B, B+C, A+C, A+B+C$$ are perfect squares?
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asked Aug 18, 2023 at 7:06
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1$\begingroup$ This is the perfect cuboid problem. See here $\endgroup$– Denis ShatrovCommented Aug 18, 2023 at 8:30
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$\begingroup$ Thank you @DenisShatrov. Could you please post this as an answer do that we can close the question? (Alternatively, I may remove it.) $\endgroup$– Fedor PetrovCommented Aug 18, 2023 at 8:54
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1 Answer
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If such $(A, B, C)$ exist, then $(\sqrt{A}, \sqrt{B}, \sqrt{C})$ are sides of a perfect cuboid (see here). Such a cuboid has not yet been found.
answered Aug 18, 2023 at 9:14