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.

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