$a,p,r,n$ are positive integers
$p$ is an odd prime
$a^n\pmod p = r$
Assume that we have two halves for $n$ values:
Starting from $r = a \,\,\,\text{to}\,\,\,r = p - 1$
The other half is from $r = p - a\,\,\,\text{to}\,\,\, r = 1$
Given $a,p$ and $r$
Is it possible to know in which half does $n$ exist, without having to find $n$ value?
Edit: Example:
For $a=2$, $p=11$, $n$ from $1$ to $10$:
First half:
$n=1, r=2=a$
$n=2, r=4$
$n=3, r=8$
$n=4, r=5$
$n=5, r=10=p-1$
Second half:
$n=6, r=9=p-a$
$n=7, r=7$
$n=8, r=3$
$n=9, r=6$
$n=10, r=1$