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An addition theorem on the cyclic group \({\mathbb Z}_{p^\alpha q^\beta}\)
The electronic journal of combinatorics, Tome 13 (2006)
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Let $n>1$ be a positive integer and $p$ be the smallest prime divisor of $n$. Let $S$ be a sequence of elements from ${\Bbb Z}_n={\Bbb Z}/n{\Bbb Z}$ of length $n+k$ where $k\geq {n\over p}-1$. If every element of ${\Bbb Z}_n$ appears in $S$ at most $k$ times, we prove that there must be a subsequence of $S$ of length $n$ whose sum is zero when $n$ has only two distinct prime divisors.
DOI : 10.37236/1147
Classification : 11B50, 11B65, 11B75 
@article{10_37236_1147,
     author = {Hui-Qin Cao},
     title = {An addition theorem on the cyclic group \({\mathbb {Z}_{p^\alpha} q^\beta}\)},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1147},
     zbl = {1165.11307},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1147/}
}
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Hui-Qin Cao. An addition theorem on the cyclic group \({\mathbb Z}_{p^\alpha q^\beta}\). The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1147

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