A set A [1, ..., N] is of the type B 2 if all sums a+b, with a b, a, b # A, are distinct. It is well known that the largest such set is of size asymptotic to N 1Â2 . For a B 2 set A of this size we show that, under mild assumptions on the size of the modulus m and on the difference N 1Â2 &| A | (the
Well Distribution of Sidon Sets in Residue Classes
✍ Scribed by Bernt Lindström
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 145 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Let Q=[Q j ] j=0 be a strictly increasing sequence of integers with Q 0 =1 and such that each Q j is a divisor of Q j+1 . The sequence Q is a numeration system in the sense that every positive integer n has a unique ``base-Q'' representation of the form n= j 0 a j (n) Q j with ``digits'' a j (n) sat
Let S q (n) denote the sum of digits of n in base q. For given pairwise coprime bases q 1 , ..., q l and arbitrary residue classes a i mod m i (i=1, ..., l), we obtain an estimate with error term O(N 1&$ ) for the quantity which extends results of J. Be sineau and establishes a conjecture of A. O.
Canonical number systems are the natural generalization of q-adic number systems to number fields. Such number systems admit a certain representation of each algebraic integer of a given number field with respect to the powers of a given base number b. The aim of this paper is to study the sum of di
Consider all the integers not exceeding x with the property that in the system number to base g all their digits belong to a given set D/[0, 1, ..., g, &1]. The distribution of these integers in residue classes to ``not very large'' moduli is studied. 1998 Academic Press SECTION 1 Throughout this pa
Let \(\mathbf{R}\) be a set of \(r\) distinct nonzero residues modulo a prime \(p\), and suppose that the random variable \(a\) is drawn with the uniform distribution from \(\{1,2, \ldots, p-1\}\). We show for all sets \(\mathbf{R}\) that \((p-2) / 2 r) \leqslant E[\min [a \mathbf{R}]] \leqslant 100