The set of solutions of a polynomial-exponential equation
The subspace theorem and applications.
The unit equation and the cluster principle
The zero-multiplicity of ternary recurrences
Torsion points on curves and common divisors of and
Triangles with two integral sides.
Trigonometric diophantine equations (On vanishing sums of roots of unity)
Trinomial Thue equations and inequalities.
Two equations for linear recurrence sequences
Two exponential diophantine equations
The equation , to be solved in non-negative rational integers , has been mentioned by Masser as an example for which there is still no algorithm to solve completely. Despite this, we find here all the solutions. The equation , to be solved in non-negative rational integers and a rational integer , has been mentioned by Corvaja and Zannier as an example for which the number of solutions is not yet known even to be finite. But we find here all the solutions too; there are in fact only six.