Let $p$ be a prime. Then $\mathrm{ord_{p}}(a)$ is defined as the least positive integer $d$ such that $p\mid a^{d}-1$.
Let $a$ and $b$ be two coprime natural numbers greater than $1$ and $c$ be a positive real number. Does there exist a prime $p$ such that $\left|\frac{\mathrm{ord_{p}}(a)}{\mathrm{ord_{p}}(b)}-c\right|<\gamma$ for some small constant $\gamma$?