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How to prove $x^3-y^3\neq z^3$ where $x$, $y$, and $z$ are whole numbers (integers greater than zero)?

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Actually, This is a special case of Fermats Last theorem where $n=3$ You can find the proof here

Proof for $n=3$ fermats last theorem

In general, Fermats last theorem states that there is no integer solutions for the equation $x^n + y^n = z^n$ where $n \geq 3$

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