History of Counterexamples to Euler's sum of powers conjecture

 - fourth powers - fifth powers-Definition: Solutions in nonzero integers of $a_1^k+\cdots+a_{k-1}^k=b^k$ with no-  common factor, $b>|a_i|$ for every $i$, and no two summands summing to zero; for-  even $k$ the summands $a_i$ are positive. This table stores the parts $a_i$ and-  $b$, and the rows with all summands positive are counterexamples to Euler's sum-  of powers conjecture CITE{WikiEuler}.+Definition: Primitive nonzero integer solutions of $a_1^k+\cdots+a_{k-1}^k=b^k$ with+  $b>|a_i|$ for every $i$ and no pair $a_i=-a_j$; for even $k$ the $a_i$ are positive.+  This table stores the parts $a_i$ and $b$. Rows with all $a_i>0$ are counterexamples+  to Euler's sum of powers conjecture CITE{WikiEuler}. Parameters:   k: