In this post, we will see the book Criteria For Divisibility by N. N. Vorob’ev. This book is Volume 16 of Popular Lectures in Mathematics series.

About the book

N. N. Vorob’ev’s Criteria for Divisibility introduces the high school or early college student to a specific number-theoretic topic and explains the general mathematical structures which underlie the particular concepts discussed. Vorob’ev discusses the ideas of well-ordered sets, partial and linear orderings, equivalence relations, equivalence classes, algorithms, and the relationship between the determinability of algorithms defined on the integers and the well-ordering principle.

The book was translated from Russian by Daniel Levine and Timothy McLarnan  was published in 1980.

Credits to original uploader.

You can get the book here.

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Contents

Preface vii

1. Divisibility of Numbers 1
2. The Divisibility of Sums and Products 17
3. Criteria for Congruence and Criteria for Divisibility 22
4. Divisibility of Powers 36
5. Proofs of Theorems 41
6. Solutions to Problems 50