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Zero Sum Properties in Groups

Angelina A. Wu (George Mason University graduate)

出版	George Mason University, 2013
URL	http://books.google.com.hk/books?id=Rh-toAEACAAJ&hl=&source=gbs_api

註釋

A conjecture by Erdős and Lemke in elementary number theory goes as follows: If d is a divisor of n and we have d divisors of n, say a1,...,a[subscript d], not necessarily distinct, we can always find a subsequence among them such that their sum is (i) divisible by d, and (ii) at most n. -- This was proved by Lemke and Kleitman to be indeed the case. They also noted that an equivalent version of their theorem, stated in terms of the additive cyclic group G = the set of integers modulo n is as follows: Every sequence of n elements of G, not necessarily distinct, contains a subsequence g1,...,g[subscript k] such that g1+...+g[subscript k] = 0 and [summation equation]