**When Snakes Collide: The Chaotic Snakes Crash That’s Tearing the Internet

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Chaotic Snakes by greenpixels_
Chaotic Snakes by greenpixels_
Chaotic Snakes by greenpixels_
Chaotic Snakes by greenpixels_
Chaotic Snakes by greenpixels_

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is a three-digit number and divisible by both 12 and 18. Thus, $\boxed{108}$ is the smallest such number.
Question: A medical researcher models vaccine efficacy cycles where a booster dose is administered every $\phi(n)$ days for a gene variant with $n = 48$. What is $\phi(48)$, Euler’s totient function value, that determines the periodicity?
Solution: Compute $\phi(48)$. First, factor $48 = 2^4 \cdot 3$. Using the totient formula:

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