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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

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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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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