Let a and b be integers and n a positive integer. Assume also that a and n have a common divisor d > 1, but that the only positive integer dividing all three of a, b, and n is 1. Show that the congruence ax ≡ b mod n has no solutions.

Let a and b be integers and n a positive integer. Assume also that a and n have a common divisor d > 1, but that the only positive integer dividing all three of a, b, and n is 1. Show that the congruence ax ≡ b mod n has no solutions.

Name: Let a and b be integers and n a positive integer. Assume also that a a
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Let a and b be integers and n a positive integer. Assume also that a and n have a common divisor d > 1, but that the only positive integer dividing all three of a, b, and n is 1. Show that the congruence ax ≡ b mod n has no solutions.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.5: Congruence Of Integers

Problem 58E: a. Prove that 10n(1)n(mod11) for every positive integer n. b. Prove that a positive integer z is...

See similar textbooks