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arXiv · 2207.12726

Ideal solutions of the Tarry-Escott Problem of degree seven

Ajai Choudhry
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Abstract

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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Ajai Choudhry. 2022-07-26. Ideal solutions of the Tarry-Escott Problem of degree seven. https://arxiv.org/abs/2207.12726

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