Vol. 26, No. 2, 1968

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The addition of residue classes modulo n

Charles Albert Ryavec

Vol. 26 (1968), No. 2, 367–373
Abstract

In the present paper, the following is proved:

Theorem. Let a1,,am be m distinct, nonzero residues modulo n, where n is any natural number and where

                 ----
√ ---     V-log-n-
m ≧ 3  6nexp {cloglogn },

where c > 0 is some large constant. Then the congruence

𝜖1a1 + ⋅⋅⋅+ 𝜖mam ≡ 0 (mod n)

is solvable with 𝜖i = 0 or 1 and not all 𝜖i = 0.

The method of proof is completely elementary, in that it is based upon well-known results concerning the addition of residues modulo a natural number n and upon results from elementary number theory.

Mathematical Subject Classification
Primary: 10.62
Milestones
Received: 27 November 1967
Published: 1 August 1968
Authors
Charles Albert Ryavec