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candyman ii farewell to the flesh - Baxtercollege

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Given that \( x + y = 100 \), we aim to find the largest possible \(\gcd(x, y)\). Let \( d = \gcd(x, y) \). Then \( x = dm \) and \( y = dn \) for some integers \( m \) and \( n \) such that \(\gcd(m, n) = 1\). Substituting into the sum, we have:

📌 dm + dn = 100 \implies d(m + n) = 100

📌 To maximize \( d \), \( m + n \) must be minimized. Since \(\gcd(m, n) = 1\), the smallest possible value for \( m + n \) is 2, achieved when \( m = 1 \) and \( n = 1 \). Thus:

📌 d imes 2 = 100 \implies d = rac{100}{2} = 50

📌 Therefore, the largest possible value of \(\gcd(x, y)\) is \(oxed{50}\).

📌 An entomologist is studying the population dynamics of a certain insect species. The population count, \( n \), is observed to be a three-digit number such that the sum of its digits is a perfect square. What is the largest possible population count?

📌 Let \( n = 100a + 10b + c \), where \( a, b, c \) are digits and \( a

📌 eq 0 \). The sum of the digits is \( a + b + c \), and we require this sum to be a perfect square. The largest three-digit number is 999, so \( a + b + c \) ranges from 1 to 27.

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