   Chapter 2.5, Problem 25E

Chapter
Section
Textbook Problem

Complete the proof of Theorem 2.23 : If a ≡ b   ( mod   n ) and x is any integer, then a + x ≡ b + x   ( mod   n ) .

To determine

To prove: If ab(modn) and x is any integer, then a+xb+x(modn)

Explanation

Given information:

ab(modn) and x is any integer.

Formula Used:

Definition: Congruence Modulo n

Let n be a positive integer, n>1. For integers x and y, x is congruent to y modulo n, if and only if xy is a multiple of n. We write xy(modn) to indicate that x is congruent to y modulo n.

Proof:

Let ab(modn) and x

Claim: a+xb+x(modn)

By using definition,

ab(modn)a

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

Evaluate the limit, if it exists. limt1t41t31

Single Variable Calculus: Early Transcendentals, Volume I

Find the general indefinite integral. t(t2+3t+2)dt

Single Variable Calculus: Early Transcendentals

The arc length function for y = x2, 1 x 3 is s(x) = a) 1x1+4x2dx b) 1x1+4t2dt c) 1x1+t4dt d) 1x1+4t4dt

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