# ON A PROBLEM OF SIDON IN ADDITIVE NUMBER THEORY, AND ON SOME RELATED PROBLEMS

@inproceedings{Ebdos2002ONAP, title={ON A PROBLEM OF SIDON IN ADDITIVE NUMBER THEORY, AND ON SOME RELATED PROBLEMS}, author={P Ebdos and Peter Tur}, year={2002} }

Let a,<&<... be a sequence of positive integers, and suppose that the suma czi+lzi (where i ,<j) are all different. Such sequences, called B, sequences by Sidont, occur in the theory of Fourier series. Suppose that n is given, and that oz < n < aX+r ; the question was raised by Sidon how large 2 can be ; that is, how many terms not exceeding n a J3, sequence can have. Put x = d(n), and denote by Q(n) the maximum of 4(n) for given n. Sidon observed that Q(n)-> en*, where c ia a positive constant…

## 160 Citations

SOME PROBLEMS ON ADDITIVE NUMBER THEORY

- Mathematics
- 2001

Dedicated to Professor A. Kotzig on the occasion of his sixtieth birthday Denote by f(n) the largest integer k for which there is a sequence 1 d al <+. . <a,< n so that all the sums ai+ ai are…

A note on Sidon-Ramsey numbers

- Mathematics
- 2021

Given a positive integer k, the Sidon-Ramsey number SR(k) is defined as the minimum n such that in every partition of [1, n] into k parts there is a part containing two pairs of numbers with the same…

On Sidon sets and asymptotic bases

- Mathematics
- 2015

Erdös conjectured the existence of an infinite Sidon sequence of positive integers which is an asymptotic basis of order 3. We progress towards this conjecture in several directions. We prove the…

On polynomials with flat squares

- Mathematics
- 2011

where R(A,n) is the number of representations of n in the form n = a1 +a2 with a1, a2 ∈ A. An old conjecture of Erdős and Turán [6] asserts that for any such infinite set A and any nonnegative…

A Numerical Note on Upper Bounds for B2[g] Sets

- MathematicsExp. Math.
- 2018

Using a numerical approach, the best upper estimates on the size of a B2[g] set in an interval of integers in the cases g = 2, 3, 4, and 5 are improved.

Continuous Ramsey Theory and Sidon Sets

- Mathematics
- 2002

A symmetric subset of the reals is one that remains invariant under some reflection x --> c-x. Given 0 D(x), then there exists a subset of [0,1] with measure x that does not contain a symmetric…

On a question of Sárközy on gaps of product sequences

- Mathematics
- 2009

Motivated by a question of Sárközy, we study the gaps in the product sequence B = A · A = {b1 < b2 < …} of all products aiaj with ai, aj ∈ A when A has upper Banach density α > 0. We prove that there…

On the supremum of the representation function of a sumset

- Mathematics
- 2014

Abstract Let A be a subset of the set of nonnegative integers ℕ ∪ {0}, and let rA (n) be the number of representations of n ≥ 0 by the sum a + b with a, b ∈ A. Define s(A):= supn≥0 r A (n) for each A…

Representation of Integers by Near Quadratic Sequences

- Mathematics
- 2012

Following a statement of the well-known Erdýos-Turan conjecture, Erdýos mentioned the following even stronger conjecture: if the n-th term an of a sequence A of positive integers is bounded byn 2 ,…

## References

SHOWING 1-2 OF 2 REFERENCES

The proof is similar to that wed by P

- Erdijs in Mitt. Tomsk Univ
- 1938

If f(a) > o for n > rt,, then hm f(n) = CD. Here we may mention that the corresponding result for g(n), the number of representation8 of n as ai a, can be proved*. The University of Pennsylvania

- If f(a) > o for n > rt,, then hm f(n) = CD. Here we may mention that the corresponding result for g(n), the number of representation8 of n as ai a, can be proved*. The University of Pennsylvania