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 Tρ (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 ≤ Tρ (11) ≤ 4.
Proceedings of the Iowa Academy of Science
© Copyright 1959 by the Iowa Academy of Science, Inc.
Real, M. Anne Cathleen
"Waring's Problem, Modulo p, and the Representation Symbol,"
Proceedings of the Iowa Academy of Science: Vol. 66:
, Article 49.
Available at: https://scholarworks.uni.edu/pias/vol66/iss1/49