Erdos P., Graham R.L. Old and New Problems and Results in Combinatorial Number Theory

L'Enseignement Mathematique, University de Geneve, 1980. — 128 p.
In the present work we will discuss various problems in elementary number theory, most of which have a combinatorial flavor. In general we will avoid classical problems, just mentioning references for the interested reader. We will almost never give proofs but on the other hand we will try to give as exact references as we can. We will restrict ourselves mostly to problems on which we worked for two reasons: (i) In order not to make the paper too long; (ii) We may know more about them than the reader.
Both the difficulty and importance of the problems discussed are very variable — some are only exercises while others are very difficult or even hopeless and may have important consequences or their eventual solution may lead to important advances and the discovery of new methods. Some of the problems we think are difficult may turn out to be trivial after all — this has certainly happened before in the history of the world with anyone who tried to predict the future.van der Waerden's Theorem and Related Topics
Covering Congruences
Unit Fractions
Bases and Related Topics
Completeness of Sequences and Related Topics
Irrationality and Transcendence
Diophantine Problems
Miscellaneous Problems
Remarks on an Earlier Paper
Added in proofIndex of Names