On the size of finite Sidon sequences

Author:
Sheng Chen

Journal:
Proc. Amer. Math. Soc. **121** (1994), 353-356

MSC:
Primary 11B83; Secondary 11B50

DOI:
https://doi.org/10.1090/S0002-9939-1994-1196162-9

MathSciNet review:
1196162

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Abstract: Let be an integer. A set of positive integers *B* is called a -sequence, or a Sidon sequence of order *h*, if all sums , where , are distinct up to rearrangements of the summands. Let be the size of the maximum -sequence contained in . We prove that

**[1]**R. C. Bose and S. Chowla,*Theorems in the additive theory of numbers*, Comment. Math. Helv.**37**(1962/1963), 141-147. MR**0144877 (26:2418)****[2]**P. Erdős and P. Turan,*On a problem in additive number theory and some related problems*, J. Number Theory**38**(1941), 191-205.**[3]**X.-D. Jia,*On finite Sidon sequences*, J. Number Theory**44**(1993), 84-92. MR**1219489 (94k:11014)****[4]**M. A. Lee,*On**sequences*, Acta Math. Sinica**34**(1991), 67-71.**[5]**B. Lindström,*A remark on*-*sequences*, J. Combin. Theory**7**(1969), 276-277. MR**0249389 (40:2634)****[6]**S. Sidon,*Ein Satz uber trigonomietrische Polynome und seine Anwendun gen in der Theorie der Fourier-Reihen*, Math. Ann.**106**(1932), 536-539. MR**1512772**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1196162-9

Keywords:
Additive number theory,
difference sets,
-sequence,
Sidon sequences

Article copyright:
© Copyright 1994
American Mathematical Society