exam2h - MATH 470(sections 501 200 Exam 2 You may use a...

• Test Prep
• 7
• 90% (10) 9 out of 10 people found this document helpful

This preview shows page 1 - 3 out of 7 pages.

MATH 470 (sections 501, 200) Exam 2 You may use a calculator provided it only has the ability to add, multiply, subtract and divide. Some facts you might find useful (mod 1729) relations 11 27 1331, 3 54 1065, 37 108 1, 37 864 1. (mod 401) relations 3 102 180 3 231 316 180 231 261 231 180 222 231 102 261 13 39 249 381 39 20 249 6 44 44 . 319 1 249 . 319 33 379 . 319 200 (mod 667) relations 3 123 653 123 2 455 123 3 604 123 4 255 123 5 16 499 3 71 499 5 236 499 40 509 499 411 584 499 493 100 499 533 6 3 . 411 1(mod 616) 5 . 493 1(mod 616) 5 . 533 1(mod 666) (mod 642401) relations 516107 . 187722 289038, 289038 2 196, 289038 3 120160, 289038 4 38416, gcd(642401 , 14)=1 gcd(642401 , 196)=1 gcd(642401 , 289038)=1 gcd(1129 , 196)=1 gcd(642401 , 289024)=1129 gcd(642401 , 289052)=569 Q1: Q2: Q3: Q4: Q5: Q6: Q7: Q8: Total:
 Describe in detail how each of the following primality tests work and illustrate your answers to the above by working out in detail the decision by each for the number n = 1729 using the possible witness a =11 . a. Fermat b. Solovay-Strassen b. Miller-Rabin (15 P OINTS )
• • • 