Waring's Problem, Modulo p, and the Representation Symbol

Authors

M. Anne Cathleen Real, Marycrest College

Document Type

Research

Abstract

The representation symbol [a,b,c] is the statement that an integer of n-ic type a is congruent to the sum of an integer of n-ic type b and an integer of n-ic type c. The symbol is extended to include any definite number of elements. New properties, together with a list of symbols involving the n-ic types of specific integers, are derived for use in studying Waring's problem, modulo p, for a particular exponent n. Let T_ρ (n) be the least number such that every integer is congruent to the sum of Tρ (n) or fewer n-ic residues. Then for primes of the form 22k + 1, k > 3, 2 ≤ T_ρ (11) ≤ 4.

Publication Date

1959

Journal Title

Proceedings of the Iowa Academy of Science

Volume

66

Issue

1

First Page

362

Last Page

364

Copyright

©1959 Iowa Academy of Science, Inc.

Language

en

File Format

application/pdf

Recommended Citation

Real, M. Anne Cathleen (1959) "Waring's Problem, Modulo p, and the Representation Symbol," Proceedings of the Iowa Academy of Science, 66(1), 362-364.
Available at: https://scholarworks.uni.edu/pias/vol66/iss1/49