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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 376.10011

**Autor: ** Alladi, K.; Erdös, Paul; Hoggatt, V.E.jun.

**Title: ** On additive partitions of integers. (In English)

**Source: ** Discrete Math. 22, 201-211 (1978).

**Review: ** Let U = **{**u_{n}**}**, u_{n+2} = u_{n+1}+u_{n}, n \geq 1, u_{1} = 1, u_{2} > u_{1}, be a linear recurrence sequence. It is shown that the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of any two distinct numbers from any one set can never be in U. Generalizations, other related problems and graph theoretic interpretation are also discussed.

**Reviewer: ** M.S.Cheema

**Classif.: ** * 11B37 Recurrences

11P81 Elementary theory of partitions

05A17 Partitions of integres (combinatorics)

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag