In number theory, a Sidon sequence (or Sidon set), named after the Hungarian mathematician Simon Sidon, is a sequence A = {a0, a1, a2, ...} of natural numbers in which all pairwise sums ai + aj (i ≤ j) are different. Sidon introduced the concept in his investigations of Fourier series.
The main problem in the study of Sidon sequences, posed by Sidon, is to find the largest number of elements a Sidon sequence A can have smaller than some given number x. Despite a large body of research, the question remained unsolved for almost 80 years. Recently, it was finally settled by J. Cilleruelo, I. Ruzsa and C. Vinuesa.
Read more about Sidon Sequence: Early Results, Infinite Sidon Sequences, Relationship To Golomb Rulers, See Also
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