Ideal solutions of the Tarry-Escott problem of degree four and a related Diophantine system
The complete ideal symmetric solution in integers of the Tarry-Escott problem of degree four, i.e., of the system of simultaneous equations \(\sum_{i=1}^5 a_i^r = \sum_{i=1}^5 b_i^r, r = 1, 2, 3, 4,\) has been obtained. In addition, a parametric ideal nonsymmetric solution has also been derived, and this nonsymmetric solution has been used to obtain a parametric solution of the Diophantine system \(\sum_{i=1}^5 a_i^r = \sum_{i=1}^5 b_i^r, r = 1, 2, 3, 4\) and 6.
scientific article; zbMATH DE number 1736561