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We present a new method to obtain infinite Sidon sequences, based on the discrete logarithm. We construct an infinite Sidon sequence A, with A(x)= x^{\sqrt 2-1+o(1)}. Ruzsa proved the existence of a Sidon sequence with similar counting function but his proof was not constructive. Our method generalizes to B_h sequences: For all h\ge 3, there is a B_h sequence A such that A(x)=x^{\sqrt{(h-1)^2+1}-(h-1)+o(1)}.Comment: Corrected typos and revised arguments, results unchange

Topics:
Mathematics - Number Theory, Mathematics - Combinatorics

Year: 2013

OAI identifier:
oai:arXiv.org:1209.0326

Provided by:
arXiv.org e-Print Archive

Downloaded from
http://arxiv.org/abs/1209.0326

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