   Chapter 8.4, Problem 3ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
1 views

# Let a=25,b=19, and n=3.Verify that 3 | ( 25 − 19 ) . Explain why 25=19(mod 3). What value of k has the property that 25=19+3k? What is the (nonnegative) remainder obtained when 25 in divided by 3? When 19 is divided by 3? Explain why 25 mod 25 mod 3=19 mod3.

To determine

(a)

To verify that 3|(2519).

Explanation

Given information:

a=25,b=19,n=3

Calculation:

Here | is the divisibility operation

To determine

(b)

To explain the reason for 2519(mod3).

To determine

(c)

The value of k for which 25=19+3k is true.

To determine

(d)

To find the nonnegative remainder when 25 is divided by 3 and also 19 is divided by 3.

To determine

(e)

To explain why 25mod3=19mod3.

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