Chapter 2.5, Problem 4TFE

Chapter
Section
Textbook Problem

Label each of the following statements as either true or false. a is congruent to b modulo n if and only if a and b yield the same remainder when each is divided by n .

To determine

Whether the statement, “a is congruent to b modulo n if and only if a and b yield the same remainder when each is divided by n” is true or false.

Explanation

Consider the statement, “a is congruent to b modulo n if and only if a and b yield the same remainder when each is divided by n.”

Let a is congruent to b modulo n.

Assume that a and b yield the different remainder r1 and r2 respectively, when each is divided by n.

Such that, a=nq1+r1 with 0r1<n and

b=nq2+r2 with 0r2<n for any q1,q2

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