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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.4 - Problem 7e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.4 - Problem 7e

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# Show that if a and m are relatively prime positive ISBN: 9780073383095 37

## Solution for problem 7E Chapter 4.4

Discrete Mathematics and Its Applications | 7th Edition

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Problem 7E

Show that if a and m are relatively prime positive integers, then the inverse of a modulo m is unique modulo m. [Hint: Assume that there are two solutions b and c of the congruence ax ? 1 (mod m). Use Theorem 7 of Section 4.3 to show that b ? c (mod m).]

Step-by-Step Solution:

Solution Step 1 We know that Inverse of a modulo m is an integer j such that Let there be two inverses of modulo m , b and c So, and By transitivity property of congruence, we get Since and Therefore, which is the unique inverse of a modulo m .

Step 2 of 1

##### ISBN: 9780073383095

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