A Thue equation is a Diophantine equation of the form
 |
in terms of an irreducible polynomial of degree 
having coefficients 
for which solutions in integers 
and 
are sought for each given constant 
with 
.
Thue (1909) proved that such an equation has only finitely many solutions, but it was not until much later that Tzanakis and de Weger (1989) gave a practical algorithm
for finding bounds on 
and 
. Although these bounds can be astronomically
large in some cases, they are typically small enough to allow an exhaustive search
for all solutions.
