Criteria for Divisibility
80 pages

© 1980
N. N. Vorob'ev's Criteria for Divisibility introduces the high school or early college student to a specific numbertheoretic topic and explains the general mathematical structures which underlie the particular concepts discussed. Vorob'ev discusses the ideas of wellordered sets, partial and linear orderings, equivalence relations, equivalence classes, algorithms, and the relationship between the determinability of algorithms defined on the integers and the wellordering principle.
All this is done comprehensively with the help of a unique plan for study which encourages the student to skip large sections of the book on first reading and return to them later. The more general and conceptually challenging material appears in small print, so that the student must have a good grasp of the numbertheoretic concepts on which the generalizations are based before making the step to generalization. The booklet provides both specific knowledge in a particular field of mathematical investigation and a fine basis on which to continue studies in mathematics.
All this is done comprehensively with the help of a unique plan for study which encourages the student to skip large sections of the book on first reading and return to them later. The more general and conceptually challenging material appears in small print, so that the student must have a good grasp of the numbertheoretic concepts on which the generalizations are based before making the step to generalization. The booklet provides both specific knowledge in a particular field of mathematical investigation and a fine basis on which to continue studies in mathematics.
Contents
Preface
1. Divisibility of Numbers
2. The Divisibility of Sums and Products
3. Criteria for Congruence and Criteria for Divisibility
4. Divisibility of Powers
5. Proofs of Theorems
6. Solutions to Problems
1. Divisibility of Numbers
2. The Divisibility of Sums and Products
3. Criteria for Congruence and Criteria for Divisibility
4. Divisibility of Powers
5. Proofs of Theorems
6. Solutions to Problems
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