Algebra putational Introduction John Scherk University of Toronto Copyright ⃝c 2009 by John Scherk Some Rights Reserved This work is licensed under the terms of the mons Attribution -- mercial -- Share Alike Canada license. The license is available at http: ///licenses/by-nc-sa// Attribution -- mercial -- Share Alike You are free: To Share -- to copy, distribute and transmit the work To Remix -- to adapt the work Under the following conditions: Attribution -- You must attribute the work in the manner spec- ified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work). mercial -- You may not use this work mercial purposes. Share Alike -- If you alter, transform, or build upon this work, you may , distribute the resulting work only under the same or similar licence to this one. With the understanding that: Waiver -- Any of the above conditions can be waived if you get permission from the copyright holder. Other Rights -- In no way are any of the following rights affected by the license: • Your fair dealing or fair use rights; • The author's moral rights; • Rights other persons may have either in the work itself or in how the work is used, such as publicity or privacy rights. Notice -- For any reuse or distribution, you must make clear to others the license terms of this work. The best way to do this is with a link to the web page http: ///licenses/by-nc-sa//. Contents Contents v Preface xi I Introduction to Groups 1 1 Congruences 3 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Divisibility Tests . . . . . . . . . . . . . . . . . . . . . . . . . 5 Divisors . . . . . . . . . . . . . . . . . . . . . . . . 9 Solving Congruences . . . . . . . . . . . . . . . . . . . . . . . 13 The Integers Modulo n . . . . . . . . . . . . . . . . . . . . . . 15 Introduction to Software . . . . . . . . . . . . .
