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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem

Label each of the following statements as either true or false.

The notation x   =   y mod n is used to indicate the unique integer x in the range 0   x   <   n such that x  -  y is a multiple of n .

To determine

Whether the statement, “The notation x=ymodn is used to indicate the unique integer x in the range 0x<n such that xy is a multiple of n.” is true or false.

Answer

Solution:

The statement, “The notation x=ymodn is used to indicate the unique integer x in the range 0x<n such that xy is a multiple of n.” is true.

Explanation

Consider the statement, “The notation x=ymodn is used to indicate the unique integer x in the range 0x<n such that xy is a multiple of n.”

The congruence notation gives for a fixed y, xy(modn) allows x to be any integer such that xy is a multiple of n, but the notation x=ymodn requires x to be the unique integer in the range 0x<n such that xy is a multiple of n.

Hence, the statement, “The notation x=ymodn is used to indicate the unique integer x in the range 0x<n such that xy is a multiple of n” is true.

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