For each of the following statements, use the definition of congruence to show why the statement is true or false. (a) 27 ≡ 9 (mod 6) (b) 71 ≡ −3 (mod 9) (c) 89 ≡ 28 (mod 5) (d) −26 ≡ 44 (mod 7)

For each of the following statements, use the definition of congruence to show why the statement is true or false. (a) 27 ≡ 9 (mod 6) (b) 71 ≡ −3 (mod 9) (c) 89 ≡ 28 (mod 5) (d) −26 ≡ 44 (mod 7)

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.2: Mathematical Induction

Problem 49E: Show that if the statement is assumed to be true for , then it can be proved to be true for . Is...

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Question

For each of the following statements, use the definition of congruence to show why the statement is true or false.
(a) 27 ≡ 9 (mod 6)
(b) 71 ≡ −3 (mod 9)
(c) 89 ≡ 28 (mod 5)
(d) −26 ≡ 44 (mod 7)

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