  In this paper, we consider three types of polynomial equations in quantum
computer: linear divisibility equation, which belongs to a special type of
binary-quadratic Diophantine equation; quadratic congruence equation with
restriction in the solution and exponential congruence equation in finite
field. Quantum algorithms based on Grover's algorithm and Shor's algorithm to
these problems are given. As for the exponential congruence equation, which has
been considered by Dam and Shparlinski \cite{dam} at 2008, a relatively simple
quantum algorithm is given here. And some other results and generalizations are
discovered.
