Let a be an algebraic integer in Q(v-37) and let A = (2,1 + V-37).Prove that either a or a – 1 is in A.

Given that, α is an integer in Q-37 lets consider α=-37⇒α-1=-37-1

Answered: Let a be an algebraic integer in…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.6: Congruence Classes

Problem 18E

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Let a be an algebraic integer in Q(v-37) and let A = (2, 1 + v-37). Prove that either a or a –- 1 is in A.