  The Tijdeman-Zagier conjecture states no integer solution exists for
$A^X+B^Y=C^Z$ with positive integer bases and integer exponents greater than 2
unless gcd$(A,B,C)>1$. Any set of values that satisfy the conjecture correspond
to a lattice point on a Cartesian graph which subtends a line in
multi-dimensional space with the origin. Properties of the slopes of these
lines in each plane are established as a function of coprimality of terms, such
as irrationality, which enable us to explicitly prove the conjecture by
contradiction.
