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Home » The decay can be modeled by the formula: - GetMeFoodie

The decay can be modeled by the formula: - GetMeFoodie

📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 The largest divisor of 2025 is 2025 itself, but then $ x + y = 1 $, which is not possible since $ x $ and $ y $ must both be positive integers. The next largest divisor is 675:

📌 We now look for coprime positive integers $ x $ and $ y $ such that $ x + y = 3 $. The pairs are $ (1,2) $ and $ (2,1) $, both of which are coprime. So $ d = 675 $ is achievable.

📌 Question: A science fiction writer is designing a virtual world where citizens log in using numbers that are perfect cubes ending in 888. What is the smallest positive integer whose cube ends in 888?

📌 So $ m = 5t + 2 $, then $ n = 25(5t + 2) + 17 = 125t + 50 + 17 = 125t + 67 $

📌 To maximize $ d $, minimize $ a + b $, where $ a, b $ are positive coprime integers.

📌 Can $ a + b $ be smaller? No, minimum is 2.

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