hello, so a staff ask me a great maths questions
there are 36 students, and during the ice breaking, they must meet each other. But for some reasons, there can only be 8 people at 1 group, what is the minimum numbers of groups will be formed?
simplify it, the rules are:
1. all 36 students must meet each other
2. only 8 students in a group
Consider the equation
$$ f(f(x)) = exp(exp(x)) $$
Valid for all real $x$ , $f(x) \neq exp(x)$ ( not identically equal everywhere ) , $f(x)$ is analytic and
$$ f(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + ... $$
Where $a_1,a_2,a_3,... > 0 $.
Find solutions for $f(x)$.
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Remarks :
I wonder ab...
Let $I$ be an interval in $\mathbb{R}.$
For $k \in \mathbb{N}$, let $g_k, h_k \in L^2 (I)$ where
$$\sum_{k \in \mathbb{N}} \left\Vert g_k \right\Vert_2^2 < \infty \quad \text{and} \quad \sum_{k \in \mathbb{N}} \left\Vert h_k \right\Vert_2^2$$
and
$$\left\Vert g \right \Vert_2 = \bigg [\int_{I...
