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The number of zero sums modulo m in a sequence of length n

Part of: Sequences and sets

Published online by Cambridge University Press:  26 February 2010

M. Kisin
M. Kisin
Affiliation:
Department of Mathematics, Fine Hall, Princeton University, Washington Road, Princeton, N.J. 08544-1000, U.S.A.
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Abstract

We prove a result related to the Erdős-Ginzburg-Ziv theorem: Let p and q be primes, α a positive integer, and m∈{pα, pαq}. Then for any sequence of integers c= {c1, c2,…, cn} there are at least

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 pα or pαq (Theorem 9).

MSC classification

Secondary: 11B75: Other combinatorial number theory
Type
Research Article
Information
Mathematika , Volume 41 , Issue 1 , June 1994 , pp. 149 - 163
Copyright
Copyright © University College London 1994

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References

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