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Consider the following pattern:

\[0, 1, 1, 2, 3, 5, 8, 13, 21, 34,\ldots\]

What is the next number in the pattern after \(34\)?

\[\large \displaystyle \dfrac{a}{\frac{b}{c}} = \dfrac{\frac{a}{b}}{c}\]

The above equation is a common mistake made when interpreting fractions.

How many ordered triplets of integers ...

Given 81 variables that satisfy

\[ 0 \leq a_1 \leq a_2 \leq \ldots \leq a_{81} \leq 1, \]

what is the maximum value of

...

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