Problem 1.(1) What are the squares modulo 4?(2) Let p be an odd prime and assume that p = a² + 62 for some a, be Z. Show thatp=1 (mod 4).(3) Show that if p is an odd prime satisfying p = 3 (mod 4), then p is irreducible in Z[i].

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Problem 1. (1) What are the squares modulo 4? (2) Let p be an odd prime and assume that p= a²+t for some a, be Z. Show that p=1 (mod 4). (3) Show that if p is an odd prime satisfying p = 3 (mod 4), then p is irreducible in Z[i).

Problem 1. (1) What are the squares modulo 4? (2) Let p be an odd prime and assume that p= a²+t for some a, be Z. Show that p=1 (mod 4). (3) Show that if p is an odd prime satisfying p = 3 (mod 4), then p is irreducible in Z[i).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Problem 1.
(1) What are the squares modulo 4?
(2) Let p be an odd prime and assume that p = a² + 62 for some a, be Z. Show that
p=1 (mod 4).
(3) Show that if p is an odd prime satisfying p = 3 (mod 4), then p is irreducible in Z[i].

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