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Infinite Sidon sequences

By Javier Cilleruelo


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
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