The Prouhet–Tarry–Escott problem, indecomposability of polynomials and Diophantine equations

In this paper, we show how the subjects mentioned in the title are related. First we study the structure of partitions of A ⊆ { 1 , ⋯ , n } in k -sets such that the first k - 1 symmetric polynomials of the elements of the k -sets coincide. Then we apply this result to derive a decomposability result...

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