This survey catalogs ideal numerical solutions for 296 PTE/GPTE/FPTE types and proposes, without complete proof, generalized Newton identities and six conjectural bounds to speed up computer searches.
Ideal solutions of the Tarry-Escott Problem of degree seven
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In this paper we obtain four new parametric ideal solutions of the Tarry-Escott problem of degree 7, that is, of the simultaneous diophantine equations, $\sum_{i=1}^8x_i^r=\sum_{i=1}^8y_i^r,\;r=1,\,2,\,\dots,\,7$. While all the known parametric solutions of the problem, with one exception, are given by polynomials of degrees $ \geq 5$, the solutions obtained in this paper are given by quartic polynomials, and are thus simpler than almost all of the known solutions.
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A survey of The Prouhet-Tarry-Escott Problem and its Generalizations
This survey catalogs ideal numerical solutions for 296 PTE/GPTE/FPTE types and proposes, without complete proof, generalized Newton identities and six conjectural bounds to speed up computer searches.