How can I calculate the arithmetic mean in a multiplicative group modulo $n$?
For example: if $n=15$, $a=8$ and $b=5$ then I want to find the mean of $a$ and $b$ as $7$. If $a$ and $b$ were real numbers then, the mean of $a$ and $b$ can be defined as the real number $\frac{a+b}{2}$. What I want is a way to calculate, from the integers $a$ and $b$ (that belong to the multiplicative group modulo $n$), the integer $[\frac{a+b}{2}]$ using only operations permited in the multiplicative group modulo $n$.