Proof of the Tijdeman-Zagier Conjecture via Slope Irrationality and Term Coprimality
Abstract
The Tijdeman-Zagier conjecture states no integer solution exists for AX+BY=CZ 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.
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