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**Some problems and results on additive and multiplicative number theory.**
*(English)*
Zbl 0472.10002

Analytic number theory, Proc. Conf., Temple Univ./Phila. 1980, Lect. Notes Math. 899, 171-182 (1981).

In this wide-ranging article, the author describes some intriguing problems that have interested him ans others, and he states some old and new conjectures. The first section deals with various questions concerning the divisors of \(n\). The second is concerned with bounds for the greatest \(k\) for which the sums \(a_i+a_j\), where \(1\leq a_1>\dots<a_k\leq n\), are distinct. The final section describes a variety of problems on squarefree integers and similarly constructed sequences, including those on the gaps between consecutive elements, and ends with an interesting theorem on squarefree integers.

For the entire collection see [Zbl 0465.00008].

For the entire collection see [Zbl 0465.00008].

Reviewer: Eira J. Scourfield (Egham)

### MSC:

11-02 | Research exposition (monographs, survey articles) pertaining to number theory |

11N05 | Distribution of primes |

11B83 | Special sequences and polynomials |

11B75 | Other combinatorial number theory |

00A07 | Problem books |