### Abstract

Following a statement of the well-known Erdo{double acute}s-Turán conjecture, Erdo{double acute}s mentioned the following even stronger conjecture: if the n-th term a_{n} of a sequence A of positive integers is bounded by αn^{2}, for some positive real constant α, then the number of representations of n as a sum of two terms from A is an unbounded function of n. Here we show that if a_{n} differs from αn^{2} (or from a quadratic polynomial with rational coefficients q(n)) by at most o(√log n), then the number of representations function is indeed unbounded.

Original language | English (US) |
---|---|

Journal | Journal of Integer Sequences |

Volume | 15 |

Issue number | 8 |

State | Published - Oct 23 2012 |

### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'Representation of integers by near quadratic sequences'. Together they form a unique fingerprint.

## Cite this

Haddad, L., & Helou, C. (2012). Representation of integers by near quadratic sequences.

*Journal of Integer Sequences*,*15*(8).