The ring Z[V2 is an ED withd(a + bv2) = |a² – 26*|.Show that the equations r – 2y? =1 and x² – 2y? =solutions.= -1 each hawe infinitely many integer

The objective is to show that equations x2-2y2=1 and x2-2y2=-1 each have infinitely many integer…

Answered: The ring Z[/2] is an ED with d(a + bv2)…

The ring Z[/2] is an ED with d(a + bv2) = |a² – 21³| . Show that the equations r² – 2y² = 1 and r² – 2y² = -1 cach have infinitely many integer solutions.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 14E: 14. Let be an ideal in a ring with unity . Prove that if then .

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Question

The ring Z[V2 is an ED with
d(a + bv2) = |a² – 26*|.
Show that the equations r – 2y? =1 and x² – 2y? =
solutions.
= -1 each hawe infinitely many integer

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