3) Show that (a + bi)º = (a – bi). Hint: for any x, y in a field containing Fp, (x+y)º = xº + yP. %3D
3) Show that (a + bi)º = (a – bi). Hint: for any x, y in a field containing Fp, (x+y)º = xº + yP. %3D
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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I need help with a problem from number theory
![(3) Show that (a + bi)P = (a – bi). Hint: for any x, y in a field containing Fp, (x + y)P = xP + yP.
%3D
(4) The norm of an element a + bi in F,[i] is
N(a + bi) = (a + bi)(a – bi) = a² + b² e F,
Show that for r, y e Fp[i], N(xy) = N (x)N(y).
(5) Deduce from (3) that N(a + bi) = (a + bi)P+l
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F79ab4db3-2e61-48d8-a012-1335c209cbe0%2F24a16f8e-269c-4c8c-9ad6-c5efa5dee06b%2Fwndez7d_processed.png&w=3840&q=75)
Transcribed Image Text:(3) Show that (a + bi)P = (a – bi). Hint: for any x, y in a field containing Fp, (x + y)P = xP + yP.
%3D
(4) The norm of an element a + bi in F,[i] is
N(a + bi) = (a + bi)(a – bi) = a² + b² e F,
Show that for r, y e Fp[i], N(xy) = N (x)N(y).
(5) Deduce from (3) that N(a + bi) = (a + bi)P+l
1
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