Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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t) This question concerns primality testing. Consider the composite number 921. Recall Fermat's Little Theorem: For any prime p and integer a, aº- p-1 = 1 mod p. 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 #1 mod n. We can use this as the basis of a simple primality test, called the Fermat Test. For a E Z921 we make the following definitions. 1) We call a a Fermat Liar for n = 921 if an-1 = 1 mod n, where a & (0, 1, n − 1). 2) We call a a Fermat Witness for n = 921 if an-11 mod n, where a ✯ (0, 1, n − 1). Please answer the following. What is the first Fermat Liar in Z921 ? b) What is the first Fermat Witness in Z921 ? c) How many Fermat Liars are in Z921 ? Remember not to count 0,1, or n - 1.
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Transcribed Image Text:t) This question concerns primality testing. Consider the composite number 921. Recall Fermat's Little Theorem: For any prime p and integer a, aº- p-1 = 1 mod p. 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 #1 mod n. We can use this as the basis of a simple primality test, called the Fermat Test. For a E Z921 we make the following definitions. 1) We call a a Fermat Liar for n = 921 if an-1 = 1 mod n, where a & (0, 1, n − 1). 2) We call a a Fermat Witness for n = 921 if an-11 mod n, where a ✯ (0, 1, n − 1). Please answer the following. What is the first Fermat Liar in Z921 ? b) What is the first Fermat Witness in Z921 ? c) How many Fermat Liars are in Z921 ? Remember not to count 0,1, or n - 1.
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