Herman, Jiří; Kučera, Radan; Šimša, Jaromír Equations and inequalities. Elementary problems and theorems in algebra and number theory. Translated from the second (1996) Czech edition by Karl Dilcher and revised by the authors. (English) Zbl 1055.00006 CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 1. New York, NY: Springer (ISBN 0-387-98942-0/hbk). x, 344 p. (1999). The authors offer to solve problems in three areas of classical elementary mathematics: equations and systems of equations of various kinds, algebraic inequalities, and elementary number theory, in particular divisibility and Diophantine equations. In each topic, brief theoretical discussions are followed by carefully worked out examples of increasing difficulty, and by exercises which range from routine to rather more challenging problems. While it emphasizes some methods that are not usually covered in beginning university courses, the book nevertheless teaches techniques and skills which are useful beyond the specific topics covered here. With approximately 330 examples and 760 exercises. Reviewer: Olaf Ninnemann (Berlin) Cited in 2 ReviewsCited in 1 Document MSC: 00A07 Problem books 11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 12-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory PDFBibTeX XMLCite \textit{J. Herman} et al., Equations and inequalities. Elementary problems and theorems in algebra and number theory. Translated from the second (1996) Czech edition by Karl Dilcher and revised by the authors. New York, NY: Springer (1999; Zbl 1055.00006) Online Encyclopedia of Integer Sequences: (9^n - 5) / 4.