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Entered Answer Preview Result 8 00 2 120 8 correct 2 correct 120 At least one of the answers above is NOT correct. (1 point) This question concerns primality testing. Consider the composite number 231. Recall Fermat's Little Theorem: For any prime p and integer a, -1 ap- = 1 mod p. incorrect n-1 It happens that the converse to FLT is often but not always true. That is, if n is composite and a is an integer, then more often than not an #1 mod n. We can use this as the basis of a simple primality test, called the Fermat Test. For a Є Z231 we make the following definitions. 1) We call a a Fermat Liar for n = 231 if an 11 mod n, where a € (0, 1, n − 1). n-1 - 2) We call a a Fermat Witness for n = 231 if a 1 mod n, where a € (0, 1, n − 1). Please answer the following. a) What is the first Fermat Liar in Z231 ? 8 b) What is the first Fermat Witness in Z231 ? 2 c) How many Fermat Liars are in Z231? Remember not to count 0,1, or n - 1. 120

Entered Answer Preview Result 8 00 2 120 8 correct 2 correct 120 At least one of the answers above is NOT correct. (1 point) This question concerns primality testing. Consider the composite number 231. Recall Fermat's Little Theorem: For any prime p and integer a, -1 ap- = 1 mod p. incorrect n-1 It happens that the converse to FLT is often but not always true. That is, if n is composite and a is an integer, then more often than not an #1 mod n. We can use this as the basis of a simple primality test, called the Fermat Test. For a Є Z231 we make the following definitions. 1) We call a a Fermat Liar for n = 231 if an 11 mod n, where a € (0, 1, n − 1). n-1 - 2) We call a a Fermat Witness for n = 231 if a 1 mod n, where a € (0, 1, n − 1). Please answer the following. a) What is the first Fermat Liar in Z231 ? 8 b) What is the first Fermat Witness in Z231 ? 2 c) How many Fermat Liars are in Z231? Remember not to count 0,1, or n - 1. 120

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Entered Answer Preview Result 8 00 2 120 8 correct 2 correct 120 At least one of the answers above is NOT correct. (1 point) This question concerns primality testing. Consider the composite number 231. Recall Fermat's Little Theorem: For any prime p and integer a, -1 ap- = 1 mod p. incorrect n-1 It happens that the converse to FLT is often but not always true. That is, if n is composite and a is an integer, then more often than not an #1 mod n. We can use this as the basis of a simple primality test, called the Fermat Test. For a Є Z231 we make the following definitions. 1) We call a a Fermat Liar for n = 231 if an 11 mod n, where a € (0, 1, n − 1). n-1 - 2) We call a a Fermat Witness for n = 231 if a 1 mod n, where a € (0, 1, n − 1). Please answer the following. a) What is the first Fermat Liar in Z231 ? 8 b) What is the first Fermat Witness in Z231 ? 2 c) How many Fermat Liars are in Z231? Remember not to count 0,1, or n - 1. 120
Transcribed Image Text:Entered Answer Preview Result 8 00 2 120 8 correct 2 correct 120 At least one of the answers above is NOT correct. (1 point) This question concerns primality testing. Consider the composite number 231. Recall Fermat's Little Theorem: For any prime p and integer a, -1 ap- = 1 mod p. incorrect n-1 It happens that the converse to FLT is often but not always true. That is, if n is composite and a is an integer, then more often than not an #1 mod n. We can use this as the basis of a simple primality test, called the Fermat Test. For a Є Z231 we make the following definitions. 1) We call a a Fermat Liar for n = 231 if an 11 mod n, where a € (0, 1, n − 1). n-1 - 2) We call a a Fermat Witness for n = 231 if a 1 mod n, where a € (0, 1, n − 1). Please answer the following. a) What is the first Fermat Liar in Z231 ? 8 b) What is the first Fermat Witness in Z231 ? 2 c) How many Fermat Liars are in Z231? Remember not to count 0,1, or n - 1. 120
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