Fermat quotients: Exponential sums, value set and primitive roots

Igor E. Shparlinski

For a prime $p$ and an integer $u$ with $\gcd (u,p)=1$, we define Fermat quotients by the conditions $$q_p(u)\equiv \frac{u^{p-1}-1}{p}(\mathrm{mod}p),0\le q_p(u)\le p-1.$$ D…