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proclamation of 1763 definition - All Square Golf

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Check divisibility by 7: \(2023 \div 7 \approx 289.0\), and \(7 \times 289 = 2023\), so 2023 is divisible by 7.

📌 Now, factor 289:

📌 \(\sqrt{289} = 17\), and \(17 \times 17 = 289\).

📌 Thus, \(2023 = 7 \times 17^2\).

📌 The divisors of 2023 are \(1, 7, 17, 49, 119, 289, 2023\). The largest divisor is 2023 itself. If \(d = 2023\), then \(x + y = 1\), which implies one of \(x\) or \(y\) is 0, contradicting \(x, y\) being positive integers. So, the largest feasible \(d\) is 289.

📌 We check: if \(d = 289\), then \(x + y = \frac{2023}{289} = 7\). We need \(\gcd(x, y) = 1\), and possible pairs \((x, y)\) are \((1, 6), (2, 5), (3, 4)\), all coprime.

📌 Thus, the largest possible value of \(\gcd(a, b)\) is \(\boxed{289}\).

📌 A game-based learning researcher, exploring geometric puzzles, asks: How many lattice points lie on the hyperbola \(xy = 100\)?

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