On additive partitions of integers |
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| Authors: | K. Alladi P. Erdös V.E. Hoggatt |
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| Affiliation: | University of California, Los Angeles, CA 90024, U.S.A.;The Hungarian Academy of Sciences, Budapest, Hungary;San Jose State University, San Jose, CA, U.S.A. |
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| Abstract: | Given a linear recurrence integer sequence U = {un}, un+2 = un+1 + ur, n ? 1, u1 = 1, u2> u1, we prove that the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of any two distinct members from any one set can never be in U. We give a graph theoretic interpretation of this result, study related problems and discuss possible generalizations. |
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