9. Let p = -1 mod 3 be prime.(a) Show that there exists d with 3d = 1 mod p – 1.(b) Show that if a³ = b_mod p if and only if a = b mod p.(c) Show that y² = x³ + 1 _mod p has exactly p+1 points (includingthe point o.).(d) Suppose that p= 6q – 1 with q also prime. Show that there existsa point p. # 00 such that q(p.) = .

Name: 9. Let p = -1 mod 3 be prime.(a) Show that there exists d with 3d = 1
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Description: 9. Let p = -1 mod 3 be prime.(a) Show that there exists d with 3d = 1 mod p – 1.(b) Show that if a³ = b_mod p if and only if a = b mod p.(c) Show that y² = x³ + 1 _mod p has exactly p+1 points (includingthe point o.).(d) Suppose that p= 6q – 1 with

As p≡-1 mod 3 Let q∈Z ,such that p=3q-1 p-1=3q+1 ⇒3(p-1)⇒gcd(p-1,3)=-1 ⇒3∈u(p-1) where, u(p-1) ={x…

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Let p = -1 mod 3 be prime. (a) Show that there exists d with 3d = 1 mod p – 1. (b) Show that if a³ = b mod p if and only if a = b mod p. (c) Show that y? = x +1 mod p has exactly p+ 1 points (including the point o.). (d) Suppose that p = 6q – 1 with q also prime. Show that there exists a point p. # ∞ such that q(p.) = 0. %3D

Let p = -1 mod 3 be prime. (a) Show that there exists d with 3d = 1 mod p – 1. (b) Show that if a³ = b mod p if and only if a = b mod p. (c) Show that y? = x +1 mod p has exactly p+ 1 points (including the point o.). (d) Suppose that p = 6q – 1 with q also prime. Show that there exists a point p. # ∞ such that q(p.) = 0. %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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