*(u pou) q. Therefore, the solutions are those integers x such that x = a (m)-1b (mod m). Example 6.21. The solutions of 3x 7 (mod 10) are given by x 3E 33.7=9 (mod 10), because o(10) = 4. 6.3 EXERCISES 1. Find a reduced residue system modulo each of the following integers. a) 6 b) 9 c) 10 d) 14 e) 16 f) 17 2. Find a reduced residue system modulo 2", where m is a positive integer. 3. Show that if c1, C2, . . , Co(m) is a reduced residue system modulo m, where m integer with m# 2, then c, + C2+ +Co(m) = 0 (mod m). ... with (a m) = (a - 1. m) = 1, then 1 iuto
*(u pou) q. Therefore, the solutions are those integers x such that x = a (m)-1b (mod m). Example 6.21. The solutions of 3x 7 (mod 10) are given by x 3E 33.7=9 (mod 10), because o(10) = 4. 6.3 EXERCISES 1. Find a reduced residue system modulo each of the following integers. a) 6 b) 9 c) 10 d) 14 e) 16 f) 17 2. Find a reduced residue system modulo 2", where m is a positive integer. 3. Show that if c1, C2, . . , Co(m) is a reduced residue system modulo m, where m integer with m# 2, then c, + C2+ +Co(m) = 0 (mod m). ... with (a m) = (a - 1. m) = 1, then 1 iuto
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 90E
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