6. (i) Solve the congruence relation 3x + 5 = 2(3 – 5x) (mod 35) for r.-(ii) If a = b (mod n) and c =d (mod n), show that ac = bd (mod n).(iii) Z39, the set of all the reduced residue classes modulo 39.

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Answered: 6. (i) Solve the congruence relation 3x…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 3E: Find all monic irreducible polynomials of degree 2 over Z3.

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6. (i) Solve the congruence relation 3x + 5 = 2(3 – 5x) (mod 35) for r. - (ii) If a = b (mod n) and c =d (mod n), show that ac = bd (mod n). (iii) Z39, the set of all the reduced residue classes modulo 39.