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Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.1 - Problem 31e
Get Full Access to Discrete Mathematics And Its Applications - 7 Edition - Chapter 4.1 - Problem 31e

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Find each of these values.a) (- 133 mod 23 + 261 mod 23)

ISBN: 9780073383095 37

Solution for problem 31E Chapter 4.1

Discrete Mathematics and Its Applications | 7th Edition

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Problem 31E

Problem 31E

Find each of these values.

a) (- 133 mod 23 + 261 mod 23) mod 23

b) (457 mod 23 · 182 mod 23) mod 23

Step-by-Step Solution:

Solution:

Step 1

Here, in this problem we have to find values of addition of two modulus.

To calculate the values, either we can calculate individually and add or we can use formula which states that, if a and b be integers and m be a positive integer.

then,

.

and

Step2

a) (- 133 mod 23 + 261 mod 23) mod 23

Here, we have  a = -133, b =261 and m = 23

Using formula,

We have,

=128 mod 23

We can write

Therefore, 128 mod 23 = 13

Therefore value of  (-133 mod 23 + 261 mod 23) mod 23 is 13.

Step 3

b) (457 mod 23 · 182 mod 23) mod 23

Here, we have  a = 457, b = 182 and m = 23

Using formula,

We have,

= 83174 mod 23

We can write

Therefore, 83174 mod 23 = 6

Therefore value of  (457 mod 23 · 182 mod 23) mod 23 is 6.

Step 2 of 3

Step 3 of 3

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