4. (i) For an odd number n, suppose that 2" # 2 mod n. Can n be a prime? Explain. This is called the base 2 primality test. (ii) Using the fact that 187 = 11-17, show that 2186174 mod 187. This shows that 187 fails the base 2 primality test. (iii) Compute 2561 mod 561. Use Fermat's little theorem and hand calculations. Does 561 pass or fail the base 2 primality test? You may use the prime factorization of 561.
4. (i) For an odd number n, suppose that 2" # 2 mod n. Can n be a prime? Explain. This is called the base 2 primality test. (ii) Using the fact that 187 = 11-17, show that 2186174 mod 187. This shows that 187 fails the base 2 primality test. (iii) Compute 2561 mod 561. Use Fermat's little theorem and hand calculations. Does 561 pass or fail the base 2 primality test? You may use the prime factorization of 561.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 58E: a. Prove that 10n(1)n(mod11) for every positive integer n. b. Prove that a positive integer z is...
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