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**Number theory. Translated from the Croatian by Petra Švob.**
*(English)*
Zbl 1472.11001

Manualia Universitatis Studiorum Zagrabiensis. Zagreb: Školska Knjiga (ISBN 978-953-0-30897-8). x, 621 p. (2021).

This book is based on teaching materials from the courses Number theory and Elementary number theory, which are taught at the undergraduate level studies at the Department of Mathematics, University of Zagreb, and the courses Diophantine equations and Diophantine approximations and applications, which were taught at the doctoral program of mathematics at that unit. This book is primarily intended for teachers and students of mathematics and related subjects at universities. It can also be useful to advanced high school students who are preparing for mathematics competitions at all levels, from the school level to international competitions, and for doctoral students and scientists in the fields of number theory, algebra and cryptography.

The book is composed by 16 chapters:

1 Introduction; 2 Divisibility; 3 Congruences; 4 Quadratic residues; 5 Quadratic forms; 6 Arithmetical functions; 7 Distribution of primes; 8 Diophantine approximation; 9 Applications of Diophantine approximation to cryptography; 10 Diophantine equations I; 11 Polynomials; 12 Algebraic numbers; 13 Approximation of algebraic numbers; 14 Diophantine equations II; 15 Elliptic curves; 16 Diophantine problems and elliptic curves.

Each chapter is partitioned into several parts and is concluded with a collection of various exercises.

This book is a beautiful invitation to number theory. It provides interesting connections between various fields of number theory. Proofs are presented in a concise form. I think that this is a useful opus for a wide branch of readership interested in number theory.

The book is composed by 16 chapters:

1 Introduction; 2 Divisibility; 3 Congruences; 4 Quadratic residues; 5 Quadratic forms; 6 Arithmetical functions; 7 Distribution of primes; 8 Diophantine approximation; 9 Applications of Diophantine approximation to cryptography; 10 Diophantine equations I; 11 Polynomials; 12 Algebraic numbers; 13 Approximation of algebraic numbers; 14 Diophantine equations II; 15 Elliptic curves; 16 Diophantine problems and elliptic curves.

Each chapter is partitioned into several parts and is concluded with a collection of various exercises.

This book is a beautiful invitation to number theory. It provides interesting connections between various fields of number theory. Proofs are presented in a concise form. I think that this is a useful opus for a wide branch of readership interested in number theory.

Reviewer: Pentti Haukkanen (Tampere)