If p = 7 (mod 8), where p is prime, show that p divides 2(p-1)/2 — 1. Deduce that 275 - 1 and 2155 -1 are composite.
If p = 7 (mod 8), where p is prime, show that p divides 2(p-1)/2 — 1. Deduce that 275 - 1 and 2155 -1 are composite.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 52E
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Transcribed Image Text:If p = 7 (mod 8), where p is prime, show that p divides 2(p-1)/2 — 1.
Deduce that 275 - 1 and 2155 -1 are composite.
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