Euler, Leonhard P.


A sextic counterexample to Euler's sum of powers conjecture ★★

Author(s): Euler

\begin{problem} Find six positive integers $x_1, x_2, \dots, x_6$ such that $$x_1^6 + x_2^6 + x_3^6 + x_4^6 + x_5^6 = x_6^6$$ or prove that such integers do not exist. \end{problem}

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