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II. For every odd prime q, define Mg = 29-1. Let p be a prime divisor of Mq. 1) Prove that ord,2 = q, and so q divides p - 1. Р 1 2) Prove that q divides P¹, and so 2(P-1)/2 = 1 (mod p). (²). 1, and so p = ±1 (mod 8). 3) Deduce that

II. For every odd prime q, define Mg = 29-1. Let p be a prime divisor of Mq. 1) Prove that ord,2 = q, and so q divides p - 1. Р 1 2) Prove that q divides P¹, and so 2(P-1)/2 = 1 (mod p). (²). 1, and so p = ±1 (mod 8). 3) Deduce that

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 51RE
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II. For every odd prime q, define Mg = 29-1. Let p be a prime divisor of Mq. 1) Prove that ord,2 = q, and so q divides p - 1. P 1 2) Prove that q divides 3) Deduce that (²) and so 2(p-1)/2 = 1 (mod p). 2 2 = = 1, and so p= ±1 (mod 8).
Transcribed Image Text:II. For every odd prime q, define Mg = 29-1. Let p be a prime divisor of Mq. 1) Prove that ord,2 = q, and so q divides p - 1. P 1 2) Prove that q divides 3) Deduce that (²) and so 2(p-1)/2 = 1 (mod p). 2 2 = = 1, and so p= ±1 (mod 8).
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