Answered: (a) 8 (mod 3) (mod 3) = (b) 7 (mod 5)…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.5: The Binomial Theorem

Problem 50E

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Modular Arithmetic (UPVOTE WILL BE GIVEN. PLEASE WRITE THE COMPLETE SOLUTIONS. NO LONG EXPLANATION NEEDED. BOX THE FINAL ANSWERS)

EVALUATE THE EXPRESSIONS IN EACH OF THE FOLLOWING TRIPLES:

(a) 8 (mod 3)
(mod 3) =
(b) 7 (mod 5)
(mod 5) =
(c) 3 (mod 4)
(mod 4)
=
||
=
(d) 16 (mod 10)
(mod 10) =
What conclusions can you draw?
12 (mod 3)
23 (mod 5)
10 (mod 4)
11 (mod 10)
=
=
=
8 +12
7+23
3.10
16 11

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please answer letter D and the What conclusion can be drawn?

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Suppose that the check digit is computed as described in Example . Prove that transposition errors of adjacent digits will not be detected unless one of the digits is the check digit. Example Using Check Digits Many companies use check digits for security purposes or for error detection. For example, an the digit may be appended to a -bit identification number to obtain the -digit invoice number of the form where the th bit, , is the check digit, computed as . If congruence modulo is used, then the check digit for an identification number . Thus the complete correct invoice number would appear as . If the invoice number were used instead and checked, an error would be detected, since .

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(a) 8 (mod 3) (mod 3) = (b) 7 (mod 5) (mod 5) = (c) 3 (mod 4) (mod 4) = || = 11 12 (mod 3) 23 (mod 5) = 10 (mod 4) = 8 +12 7+23 3.10