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Home » The diagonal of the square is the diameter of the circumscribed circle. Using the Pythagorean theorem: - AMAZONAWS

The diagonal of the square is the diameter of the circumscribed circle. Using the Pythagorean theorem: - AMAZONAWS

📅 March 11, 2026 👤 scraface
Mar 11, 2026
The diagonal of the square is the diameter of the circumscribed circle. Using the Pythagorean theorem:

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📌 Thus, the only lattice points are $(\pm 12, 0)$.
📌 $y = \pm5$: $25x^2 = 144(25) + 3600 = 3600 + 3600 = 7200$, $x^2 = 288$, not square.
📌 First, observe $3^1 = 3$, $3^2 = 9 \equiv 1 \pmod{8}$, so the powers of 3 mod 8 cycle every 2: $3, 1, 3, 1, \dots$

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