Number theory solve in one hour plz (it is completed i don't have more information it is complete question) Q3(solve b part only) I need hundred percent soloution plz plz 3. (a) Use Euler's criterion to determine the Legendre symbol (7).(b) Use Algorithm 2.5 from the Unit 6 notes to determine the Legendre symbol(5).

Answered: Image /qna-images/answer/a89b863c-a3ec-4029-bb55-a6f69bc614af.jpg

Answered: (b) Use Algorithm 2.5 from the Unit 6…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.4: Complex And Rational Zeros Of Polynomials

Problem 46E

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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 .
When we divide a polynomial P(x) by a divisor D(x), the Division Algorithm tells us that we can always obtain a quotient Q(x) and a remainder R(x). State two forms in which the result of this division can be written.

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(b) Use Algorithm 2.5 from the Unit 6 notes to determine the Legendre symbol 163 (157).