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# Show that if a. b, k. and m are integers such that k ? 1, ISBN: 9780073383095 37

## Solution for problem 41E Chapter 4.1

Discrete Mathematics and Its Applications | 7th Edition

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Problem 41E

Show that if a. b, k. and m are integers such that k ≥ 1, m ≥ 2, and a ≡ b (mod m), then ak ≡ bk(mod m).

Step-by-Step Solution:

Step 1</p>

In this problem we have to show that if a. b, k. and m are integers such that

k ≥ 1, m ≥ 2, and a ≡ b (mod m),

then ak ≡ bk(mod m).

Step 2</p>

ak ≡ bk(mod m) states that is congruent to bk(mod m).

Or, in other word we can say  m divides integer and we get another integer, say quotient q.

In mathematical form we can write When we expand then we get, Let, which is also an integer.

we have Therefore we can write ak ≡ bk(mod m) as . ………………….(1)

Step 3 of 3

##### ISBN: 9780073383095

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