Duverney, Daniel Number theory. An elementary introduction through Diophantine problems. (English) Zbl 1228.11001 Monographs in Number Theory 4. Hackensack, NJ: World Scientific (ISBN 978-981-4307-45-1/hbk; 978-981-4307-46-8/pbk). xii, 335 p. (2010). A very “fresh” look into Number Theory and especially into diophantine problems, through a very interesting and appealing structure is presented. Indeed, the structure of the content is unique and follows five different but not always independent paths. Having as common start the diophantine approximation the representations of real numbers, continued fractions and PadĂ© approximants take the lead, together with quadratic fields and algebraic numbers. Then, the above are properly filled up with sums of squares, arithmetical functions, number fields, ideals and transcendence methods. The flow of the content of each chapter is very smooth and connected, giving “delightful” results. Reviewer: Panayiotis Vlamos (Athens) Cited in 9 Documents MSC: 11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 11Dxx Diophantine equations 11Jxx Diophantine approximation, transcendental number theory Keywords:number theory; Diophantine problems; quadratic fields; algebraic numbers PDFBibTeX XMLCite \textit{D. Duverney}, Number theory. An elementary introduction through Diophantine problems. Hackensack, NJ: World Scientific (2010; Zbl 1228.11001) Online Encyclopedia of Integer Sequences: Decimal expansion of Sum_{k>=1} 1/F(k) where F(k) is the k-th Fibonacci number A000045(k). Decimal expansion of x = 3*Sum_{n in E} 1/10^n where E is the set of numbers whose base-4 representation consists of only 0’s and 1’s.