#### 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

© Copyright 1959 by the 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