a) Show that 2340 ≡ 1 (mod 11) by Fermat’s little theorem and noting that 2340 = (210)34.b) Showthat 2340 ≡ 1 (mod 31) using the fact that 2340 = (25)68 = 3268.c) Conclude from parts (a) and (b) that 2340 ≡ 1 (mod 341).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 36E
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a) Show that 2340 ≡ 1 (mod 11) by Fermat’s little theorem and noting that 2340 = (210)34.
b) Showthat 2340 ≡ 1 (mod 31) using the fact that 2340 = (25)68 = 3268.
c) Conclude from parts (a) and (b) that 2340 ≡ 1 (mod 341).

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