## Combinatorial Number Theory: Proceedings of the 'Integers Conference 2005' in Celebration of the 70th Birthday of Ronald Graham, Carrollton, Georgia, USA, October 27-30, 2005This carefully edited volume contains selected refereed papers based on lectures presented by many distinguished speakers at the "Integers Conference 2005", an international conference in combinatorial number theory. The conference was held in celebration of the 70th birthday of Ronald Graham, a leader in several fields of mathematics. |

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### Contents

R Graham | 2 |

G Apel R Blecksmith and J Brillhart | 23 |

R Balasubramanian and G Bhowmik | 61 |

Baruah and J Bora | 81 |

Trifonov and S E Behum | 103 |

F Chung and R Graham | 121 |

E Croot I Ruzsa and T Schoen | 157 |

J Fox V Jungic and R Radoicic | 179 |

N Hindrnan | 265 |

B Hopkins and J A Sellers | 299 |

T Komatsu | 315 |

T LeSaulnier and A Robertson | 333 |

F | 347 |

Matthews and R S Robinson | 363 |

J Nesetfil and O Serra | 381 |

K OBryant | 403 |

A S Fraenkel | 199 |

Some of my favorite problems in Ramsey theory | 229 |

S Heubach T Mansour | 243 |

P Stanica | 431 |

Zeilberger | 455 |

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3-coloring abelian group arithmetic progressions ascending wave bent functions binary sequence c(px Cayley graph coefficients combinatorial compositions compute conjecture constraints contains Corollary covering number defined different colors Dirichlet density EGZ theorem elements Email entries equation Erdos exists F. R. K. Chung finite forbidden ratios free of monochromatic function graph Graph Theory guidelines Hence image partition regular implies induced subgraphs induction hypothesis infinite Janos Bolyai Lemma length linear Mathematics Subject Classification matrix Mersenne prime minimal colorings mod 2 identities monochromatic solution multiple non-zero rational number nonnegative integer Note Number Theory partition regular permutation polynomial positive integer prime prime radical problem proof of Theorem Proposition prove Q2 identities Rado Ramsey theory real numbers result Rogers-Ramanujan Ron Graham satisfies Search Algorithm Section semigroups Step subset Suppose triangle triples vector vertex Waerden zero-sum