We denote by $p(n)$ the largest integer $p \geqslant 1$ such that $E$ admits an H-system of cardinality $p$. Determine $p(n)$ as a function of the unique integer $d \in \mathbb{N}$ such that $n$ can be written as $n = 2^d m$ with $m$ odd.
We denote by $p(n)$ the largest integer $p \geqslant 1$ such that $E$ admits an H-system of cardinality $p$.\\
Determine $p(n)$ as a function of the unique integer $d \in \mathbb{N}$ such that $n$ can be written as $n = 2^d m$ with $m$ odd.