### Abstract

If A is a set of positive integers, let R_{1} (n) be the number of solutions of a + a′ = n, a, a′ ∈ A, and let R_{2}(n) and R_{3}(n) denote the number of solutions with the additional restrictions a <a′, and a ≤ a′ respectively. The monotonicity properties of the three functions R_{1}(n), R_{2}(n), and R_{3}(n) are studied and compared. Copyright Clearance Centre, Inc.

Original language | English |
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Pages (from-to) | 129-138 |

Number of pages | 10 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 72 |

Issue number | 1 |

Publication status | Published - Aug 2005 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the Australian Mathematical Society*,

*72*(1), 129-138.

**On the monotonicity properties of additive representation functions.** / Chen, Yong Gao; Sárközy, A.; Sós, Vera T.; Tang, Min.

Research output: Contribution to journal › Article

*Bulletin of the Australian Mathematical Society*, vol. 72, no. 1, pp. 129-138.

}

TY - JOUR

T1 - On the monotonicity properties of additive representation functions

AU - Chen, Yong Gao

AU - Sárközy, A.

AU - Sós, Vera T.

AU - Tang, Min

PY - 2005/8

Y1 - 2005/8

N2 - If A is a set of positive integers, let R1 (n) be the number of solutions of a + a′ = n, a, a′ ∈ A, and let R2(n) and R3(n) denote the number of solutions with the additional restrictions a 1(n), R2(n), and R3(n) are studied and compared. Copyright Clearance Centre, Inc.

AB - If A is a set of positive integers, let R1 (n) be the number of solutions of a + a′ = n, a, a′ ∈ A, and let R2(n) and R3(n) denote the number of solutions with the additional restrictions a 1(n), R2(n), and R3(n) are studied and compared. Copyright Clearance Centre, Inc.

UR - http://www.scopus.com/inward/record.url?scp=27144485364&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=27144485364&partnerID=8YFLogxK

M3 - Article

VL - 72

SP - 129

EP - 138

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

SN - 0004-9727

IS - 1

ER -