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a) Find the smallest positive integer a in the encryption function f(x) = (ax + 7) mod 26,0 ≤ x ≤ 25, such that the function encodes the letter "H" by "C". Use the function to encrypt the message "NEED HELP". b) Prove that: If n is an integer that is not a multiple of 3, then n² = 1 mod 3.

a) Find the smallest positive integer a in the encryption function f(x) = (ax + 7) mod 26,0 ≤ x ≤ 25, such that the function encodes the letter "H" by "C". Use the function to encrypt the message "NEED HELP". b) Prove that: If n is an integer that is not a multiple of 3, then n² = 1 mod 3.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
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a) Find the smallest positive integer a in the encryption function f(x) = (ax + 7) mod 26,0 ≤ x ≤ 25, such that the function encodes the letter "H" by "C". Use the function to encrypt the message "NEED HELP". b) Prove that: If n is an integer that is not a multiple of 3, then n² = 1 mod 3.
Transcribed Image Text:a) Find the smallest positive integer a in the encryption function f(x) = (ax + 7) mod 26,0 ≤ x ≤ 25, such that the function encodes the letter "H" by "C". Use the function to encrypt the message "NEED HELP". b) Prove that: If n is an integer that is not a multiple of 3, then n² = 1 mod 3.
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