Exercise 4.4.7. Let n be odd. Prove that if we divide n² by 8, then the remainder is always 1. Exercise 4.4.8. Let n>1. Define R on Z by a Rb iff n | b-a. (a) Show that R is an equivalence relation. (b) Use the division algorithm to describe the corresponding partition.
Exercise 4.4.7. Let n be odd. Prove that if we divide n² by 8, then the remainder is always 1. Exercise 4.4.8. Let n>1. Define R on Z by a Rb iff n | b-a. (a) Show that R is an equivalence relation. (b) Use the division algorithm to describe the corresponding partition.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 16E
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