(a) Find 2 solutions in positive integers to the equation z - 26y? = 10.%3D(b) Find two distinct factorizations of 10 into irreducible elements in Z[V26] and hence deduce that Z[v26] is nota unique factorization domain.(c) Let p e N be a prime number, p=5 mod 12. Show that if p|(r + ry + y), for some z, y E Z thenP|(z + zy + y).

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Answered: (a) Find 2 solutions in positive…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter9: Polynomial And Rational Functions

Section9.2: Remainder And Factor Theorems

Problem 53PS

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(a) Find 2 solutions in positive integers to the equation z - 26y? = 10. %3D