Solve Question 5 showing detailly all the steps with including all explanationsSolution should be typewritten with the help of a computer keyboard! 4. Find d, thegcd (2695, 1547).Hence or otherwise, express in the form2695p + 1547q = d,p,q E ZSolve for x,54x = 7(mod31).5. Solve completely the equationz* – 1 = 0The solution set S, of the equation z* = 1 is a Group under multiplication of complexnumbers.i)ii)State the identity element of the element in this groupFind the inverse of each element.The set T = {3,6,9,12} under multiplication modulo 15 also forms a Group.iii)iv)Find the identity element and the inverse of each element.Establish an isomorphism S =T

2695 = 1547(1) + 1148 1547 = 1148(1)+399 1148 = 399(2) + 350 399 = 350(1) + 49 350 = 49(7) + 7…

Answered: 4. Find d, the gcd (2695, 1547). Hence…

4. Find d, the gcd (2695, 1547). Hence or otherwise, express in the form 2695p + 1547q = d, p,q E Z Solve for x, 54x = 7(mod31).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.3: Divisibility

Problem 30E: Let be as described in the proof of Theorem. Give a specific example of a positive element of .

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Question

Solve Question 5 showing detailly all the steps with including all explanations

Solution should be typewritten with the help of a computer keyboard!

4. Find d, the
gcd (2695, 1547).
Hence or otherwise, express in the form
2695p + 1547q = d,
p,q E Z
Solve for x,
54x = 7(mod31).
5. Solve completely the equation
z* – 1 = 0
The solution set S, of the equation z* = 1 is a Group under multiplication of complex
numbers.
i)
ii)
State the identity element of the element in this group
Find the inverse of each element.
The set T = {3,6,9,12} under multiplication modulo 15 also forms a Group.
iii)
iv)
Find the identity element and the inverse of each element.
Establish an isomorphism S =T

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