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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 2unless gcd$(A,B,C)>1$. Any set of values that satisfy the conjecture correspondto a lattice point on a Cartesian graph which subtends a line inmulti-dimensional space with the origin. Properties of the slopes of theselines in each plane are established as a function of coprimality of terms, suchas irrationality, which enable us to explicitly prove the conjecture bycontradiction.

Proof of the Tijdeman-Zagier Conjecture via Slope Irrationality and Term Coprimality