It is proved that there is no Sidon set selected from {1, 2, ... , N} whose sum set contains c(1)N(1/2) consecutive integers, but it may contain c(2)N(1/3) consecutive integers. Moreover, it is shown that a finite Sidon set cannot be well-covered by generalized arithmetic progressions.
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Univ. Lille, CNRS, UMR 8524, Laboratoire Paul Painlevé, Lille,F-59000, FranceUniv. Lille, CNRS, UMR 8524, Laboratoire Paul Painlevé, Lille,F-59000, France
Forey, Arthur
Fresán, Javier
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CMLS, École polytechnique, Palaiseau,F-91128 cedex, FranceUniv. Lille, CNRS, UMR 8524, Laboratoire Paul Painlevé, Lille,F-59000, France
Fresán, Javier
Kowalski, Emmanuel
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D-MATH, ETH Zürich, Rämistrasse 101, Zürich,CH-8092, SwitzerlandUniv. Lille, CNRS, UMR 8524, Laboratoire Paul Painlevé, Lille,F-59000, France
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Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, BrazilUniv Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, Brazil
Kohayakawa, Yoshiharu
Lee, Sang June
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Kyung Hee Univ, Dept Math, Seoul, South KoreaUniv Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, Brazil
Lee, Sang June
Moreira, Carlos Gustavo
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Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, BrazilUniv Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, Brazil
Moreira, Carlos Gustavo
Rodl, Vojtech
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Emory Univ, Dept Math, Atlanta, GA 30322 USAUniv Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, Brazil