On the size of finite Sidon sets

UDC 519.1 A Sidon set (also called a Golomb ruler) is a B 2 sequence and a 1 -thin set is a set of integers containing no nontrivial solutions to the equation a + b = c + d . We improve the lower bound for the diameter of a Sidon set with k elements, namely, if k is sufficiently large and 𝒜 is a Sidon set with k elements, then ⅆ i a m ( 𝒜 ) ≥ k 2 - 1.99405 k 3 / 2 . Alternatively, if n is sufficiently large, then the cardinality of the largest subset of { 1,2 , … , n } , which is a Sidon set, does not exceed n 1 / 2 + 0.99703 n 1 / 4 .