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- W3037208752 abstract "Erdos conjectured the existence of an infinite Sidon sequence of positive integers which is also an asymptotic basis of order 3. We make progress towards this conjecture in several directions. First we prove the conjecture for all cyclic groups Z_N with N large enough. In second place we prove by probabilistic methods that there is an infinite B_2[2] sequence which is an asymptotic basis of order 3. Finally we prove that for all c>0 there is a Sidon sequence which is an asymptotic basis of order 3+c,that is to say, any positive sufficiently large integer n can be written as a sum of 4 elements of the sequence, one of them smaller than n^c." @default.
- W3037208752 created "2020-07-02" @default.
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- W3037208752 date "2013-04-19" @default.
- W3037208752 modified "2023-09-27" @default.
- W3037208752 title "Sidon Basis" @default.
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