Inaug.-diss.--Georg-August-Universität. / Cover title. Vita.

Thesis (Master's)--St. Petersburg. / Translation of title: Some applications of continuous parameters to the theory of numbers.

Inaug.-diss.--Leipzig.

Inaug.-diss.--Kaiser-Wilhelms-Universität.

Thesis (Ph. D.)--University of Texas at Austin, 2005. / Supervisor: Fernando Rodriguez-Villegas. Vita. Includes bibliographical references.

[No abstract available] / Science, Faculty of / Mathematics, Department of / Graduate

[No abstract available] / Science, Faculty of / Mathematics, Department of / Graduate

The numbers 1, 2, and 6 have the same sum and same sum of squares as 0, 4, 5. These two sets are solutions of degree 2 of the Tarry-Escott problem. This problem of finding sets of integers having equal sums of like powers has been investigated for at least two hundred years and we have presented most of the general results. For any given k there exist solutions in integers of the system of equations (formula omitted) any solution will be composed of a set and a permutation of the set; such solutions are called trivial. Many writers have attempted to provide non-trivial solutions for the optimum case where s = k + 1. These so called ideal solutions exist for all k≦9 but no such solutions have been found for k≧10. We have been interested in providing solutions where s is smaller than for previous known examples, and have generated such solutions using a digital computer. Some of our results also apply to an extension of the Tarry-Escott problem in view of a result concerning bounds for this problem. / Science, Faculty of / Mathematics, Department of / Graduate

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