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Home » Thus, the minimum value is: - High Altitude Science

Thus, the minimum value is: - High Altitude Science

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 First, factor 100:

📌 \(100 = 2^2 \times 5^2\), so the number of positive divisors is \((2+1)(2+1) = 9\).

📌 The positive divisors are: \(1, 2, 4, 5, 10, 20, 25, 50, 100\).

📌 Each positive divisor \(d\) gives a solution \((d, 100/d)\), and each negative divisor \(-d\) gives \((-d, -100/d)\).

📌 Thus, total lattice points: \(2 \times 9 = 18\) (each positive divisor contributes two points: one in positive quadrant, one in negative).

📌 We verify: for each of the 9 positive \(d\), \((d, 100/d)\) and \((-d, -100/d)\) are distinct lattice points.

📌 Therefore, the total number of lattice points on \(xy = 100\) is \(\boxed{18}\).

📌 A geneticist analyzing periodic patterns in modular arithmetic asks: What is the remainder when the sum \(1^3 + 2^3 + 3^3 + \cdots + 10^3\) is divided by 11?

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