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The number of zero sums modulo m in a sequence of length n
Author(s) -
Kisin M.
Publication year - 1994
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300007257
Subject(s) - mathematics , modulo , sequence (biology) , combinatorics , integer (computer science) , zero (linguistics) , primitive root modulo n , discrete mathematics , linguistics , philosophy , genetics , biology , computer science , programming language
We prove a result related to the Erdős‐Ginzburg‐Ziv theorem: Let p and q be primes, α a positive integer, and m ∈{ p α , p α q }. Then for any sequence of integers c = { c 1 , c 2 ,…, c n } there are at least(⌊ 1 2 n ⌋m) + (⌈ 1 2 n ⌉m)subsequences of length m , whose terms add up to 0 modulo m (Theorem 8). We also show why it is unlikely that the result is true for any m not of the form p α or p α q (Theorem 9).