Elementary Number Theory (5th Edition)

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Unformatted text preview: Course: Math 4150 (Spring’10) – Some Sample Questions Instructor : Prasad Tetali, office: Skiles 234, email: tetali@math.gatech.edu Somewhat on the harder side! 1. Show that there are infinitely many primes in the sequence 3n + 2. 2. Show that if a3 |b2 , then a|b. 3 (a) Show that any two consecutive integers are relatively prime. (b) Let S be any subset of n + 1 elements of the set {1, 2, . . . , 2n}. Show that there exist two elements of S which are relatively prime. (Hint: Use the pigeon-hole principle). 4. Find an integer solution to ax ≡ b(mod n), where a = 585, n = 429, and b = 78. 5. Find an integer which is congruent to 5 mod 7, but is congruent to 8 mod 9. ...
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This note was uploaded on 02/15/2010 for the course MATH 4150 taught by Professor Prasadtetali during the Spring '10 term at Georgia Institute of Technology.

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