  Let $V$ be an absolutely irreducible affine variety over $\mathbb{F}_p$. A
Lehmer point on $V$ is a point whose coordinates satisfy some prescribed
congruence conditions, and a visible point is one whose coordinates are
relatively prime. Asymptotic results for the number of Lehmer points and
visible points on $V$ are obtained, and the distribution of visible points into
different congruence classes is investigated.
