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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
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

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