Is there a method to find all solutions to a Diphantine equation of the form $Ax^3-By^3=C$, where $A,B,C\in\mathbb{Z}$? The quadratic case is the famous Pell's equation, but I am unsure about how to solve this cubic case. According to WolframMathWorld, Thue showed that it has only a finite number of solutions, which seems to be related, but I could not find the proof.
2026-04-24 20:21:21.1777062081
Cubic Diphantine equations of the form $Ax^3-By^3=C$.
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