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s 19 a prime in the Eisenstein integers? is 79? If they are, explain why, if not, display a factorization into primes. (b) Show that if p is a prim

s 19 a prime in the Eisenstein integers? is 79? If they are, explain why, if not, display a factorization into primes. (b) Show that if p is a prim

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 50E: Show that if the statement 1+2+3+...+n=n(n+1)2+2 is assumed to be true for n=k, the same equation...
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(12.1) Primes in the Eisenstein integers:
(a) Is 19 a prime in the Eisenstein integers? is 79? If they are, explain why,
if not, display a factorization into primes.
(b) Show that if p is a prime in the rational integers and p ≡ 2 mod 3, then
p is also a prime in the Eisenstein integers.

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