   Chapter 2.5, Problem 47E

Chapter
Section
Textbook Problem

In the congruences a x ≡ b ( m o d   n ) in Exercises 40 − 53 , a and n may not be relatively prime. Use the results in Exercises 38 and 39 to determine whether there are solutions. If there are, find d incongruent solutions modulo n . 24 x + 5 ≡ 50   ( m o d  348 )

To determine

Whether there are solutions of congruence 24x+550(mod348). If there are, find d incongruent solutions modulo 348.

Explanation

Formula used:

i) For d=(a,n), where n>1, if there is a solution to axb(modn), then d divides b.

ii) Theorem: Addition and Multiplication Properties:

If ab(modn) and x is any integer, then

a+x=b+x(modn) and ax=bx(modn).

Explanation:

Given, 24x+550(mod348).

By adding property of congruence’s,

24x+5+(5)(50+(5))(mod348)

24x45(mod348)<

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

In Exercises 19-24, find the functions f + g, f g, fg, and fg. 22. f(x) =1x2+1; g(x) = 1x21

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Differentiate the functions in Problems 3-20. 11.

Mathematical Applications for the Management, Life, and Social Sciences

Find y and y. y=1sect

Single Variable Calculus: Early Transcendentals, Volume I

Identify the four steps of a hypothesis test as presented in this chapter.

Statistics for The Behavioral Sciences (MindTap Course List)

Given:12. Prove: ABAC=BECD

Elementary Geometry for College Students

π does not exist

Study Guide for Stewart's Multivariable Calculus, 8th

What is the partial fraction form of ?

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 