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Deduce from Q2 that if an integer N can be written as N = x² + ny² , and if a prime number q | N can be written as q = z² + nw² (w, x, y, z E Z), then the integer can also be written as a? + nb² ( а, bE Z).

Deduce from Q2 that if an integer N can be written as N = x² + ny² , and if a prime number q | N can be written as q = z² + nw² (w, x, y, z E Z), then the integer can also be written as a? + nb² ( а, bE Z).

Advanced Engineering Mathematics
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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Q2

for all ?,?,?,?,?∈ℤ:

(?^2+??^2)(?^2+??^2)=(??±???)^2+?(??∓??)^2.

Deduce from Q2 that if an integer N can be written as N = x² + ny² , and if a prime number q | N can a² + nb² ( be written as q = z2 + nw? (w, x, y, z E Z), then the integer N can also be written as N a, b e Z).
Transcribed Image Text:Deduce from Q2 that if an integer N can be written as N = x² + ny² , and if a prime number q | N can a² + nb² ( be written as q = z2 + nw? (w, x, y, z E Z), then the integer N can also be written as N a, b e Z).
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