### Abstract

A very special case of one of the theorems of the authors states as follows: Let 1≤a_{1}≤a_{2}≤... be an infinite sequence of integers for which all the sums a_{i}+a_{j}, 1≤i≤j, are distinct. Then there are infinitely many integers k for which 2 k can be represented in the form a_{i}+a_{j} but 2 k+1 cannot be represented in this form. Several unsolved problems are stated.

Original language | English |
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Pages (from-to) | 183-197 |

Number of pages | 15 |

Journal | Monatshefte fur Mathematik |

Volume | 102 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1986 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Monatshefte fur Mathematik*,

*102*(3), 183-197. https://doi.org/10.1007/BF01294598

**Problems and results on additive properties of general sequences, V.** / Erdős, P.; Sárközy, A.; Sós, V. T.

Research output: Contribution to journal › Article

*Monatshefte fur Mathematik*, vol. 102, no. 3, pp. 183-197. https://doi.org/10.1007/BF01294598

}

TY - JOUR

T1 - Problems and results on additive properties of general sequences, V

AU - Erdős, P.

AU - Sárközy, A.

AU - Sós, V. T.

PY - 1986/9

Y1 - 1986/9

N2 - A very special case of one of the theorems of the authors states as follows: Let 1≤a1≤a2≤... be an infinite sequence of integers for which all the sums ai+aj, 1≤i≤j, are distinct. Then there are infinitely many integers k for which 2 k can be represented in the form ai+aj but 2 k+1 cannot be represented in this form. Several unsolved problems are stated.

AB - A very special case of one of the theorems of the authors states as follows: Let 1≤a1≤a2≤... be an infinite sequence of integers for which all the sums ai+aj, 1≤i≤j, are distinct. Then there are infinitely many integers k for which 2 k can be represented in the form ai+aj but 2 k+1 cannot be represented in this form. Several unsolved problems are stated.

UR - http://www.scopus.com/inward/record.url?scp=22944490162&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22944490162&partnerID=8YFLogxK

U2 - 10.1007/BF01294598

DO - 10.1007/BF01294598

M3 - Article

AN - SCOPUS:22944490162

VL - 102

SP - 183

EP - 197

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 3

ER -