1. The problem asks if there are any whole number solutions $(x, y, z)$ to the equation $$x^n + y^n = z^n$$ where $n$ is a whole number greater than 2. 2. This is a famous problem known as Fermat's Last Theorem. 3. Fermat's Last Theorem states that there are no three positive integers $x, y, z$ that satisfy the equation $$x^n + y^n = z^n$$ for any integer $n > 2$. 4. The theorem was conjectured by Pierre de Fermat in 1637 and remained unproven for over 350 years. 5. It was finally proven by Andrew Wiles in 1994 using advanced techniques in number theory and algebraic geometry. 6. Therefore, the answer is that there are no whole number solutions to the equation for any whole number $n > 2$. 7. In summary, Fermat's Last Theorem guarantees no solutions exist for $n > 2$ in whole numbers. Final answer: No whole number solutions exist for $x^n + y^n = z^n$ when $n$ is a whole number greater than 2.