# exam2f - MATH 470 Exam 2 You may use a calculator provided...

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MATH 470 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 1271) relations 2 635 993, 3 635 150, 23 635 1270, (mod 347) relations 8 339 334 8 166 3 137 . 8 55 137 . 8 2 93 137 . 8 3 50 137 . 8 4 54 137 . 8 5 77 (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:
[1] 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 = 1271 using the possible witness a =23 . a. Fermat b. Solovay-Strassen (12 P OINTS )