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Home » Prenez le logarithme naturel : \( \ln(0.2) = -0.1t \). - Abu Waleed Tea

Prenez le logarithme naturel : \( \ln(0.2) = -0.1t \). - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Question:** A philosopher of science reflects on the elegance of symmetry and periodicity, drawing parallels to number theoretic identities. What is the greatest common divisor of $2^{10} - 1$ and $2^{15} - 1$?

📌 Here, \( a = 10 \), \( b = 15 \), so:

📌 \gcd(10, 15) = 5

📌 \gcd(2^{10} - 1, 2^{15} - 1) = 2^5 - 1 = 32 - 1 = 31

📌 The greatest common divisor is \(\boxed{31}\).

📌 Question:** A zoologist tracking nocturnal animal activity cycles notices behavioral patterns recurring every 9 days, prompting interest in numerical periodicity. What is the smallest three-digit number that is divisible by both 9 and 12?

📌 We seek the least three-digit number divisible by \( \text{lcm}(9, 12) \).

📌 First, compute the LCM:

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