Finding finite -sequences with larger

Author:
Zhen Xiang Zhang

Journal:
Math. Comp. **63** (1994), 403-414

MSC:
Primary 11Y55; Secondary 11B75

DOI:
https://doi.org/10.1090/S0025-5718-1994-1223235-2

MathSciNet review:
1223235

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Abstract | References | Similar Articles | Additional Information

Abstract: A sequence of positive integers is called a (finite) -sequence, or a (finite) Sidon sequence, if the pairwise differences are all distinct. Let

*m*-element -sequences. Erdős and Turán ask if . In this paper we give an algorithm, based on the Bose-Chowla theorem on finite fields, for finding a lower bound of and a

*p*-element -sequence with equal to this bound, taking bit operations and requiring storage, where

*p*is a prime. A search for lower bounds of for is given, especially , where is the

*i*th prime.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1994-1223235-2

Keywords:
-sequences,
Erdős-Turán conjecture,
Bose-Chowla theorem,
finite fields,
algorithms

Article copyright:
© Copyright 1994
American Mathematical Society