Avalg homework A fall 2006
This homework is due 3/11. It should be done individually and handed in at the beginning of the homework session. You should be prepared to present your homework orally in class. This is part of the examination and you have to attend the homework session to get credit for your homework. Solutions handed in late are not accepted and will not be graded.
1. Compute the greatest common divisor gcd(627, 1001) by hand. (5p)
2. Use the Sieve of Eratosthenes to make a list of all primes up to 50. (5p)
3. Prove that there are infinitely many primes of the form 6x - 1, where x is a positive integer. (5p)
4. Prove that if n > 4 is composite then (n - 1)! = 0 (mod n). (5p)
5. Give a complete list of integer solutions to the equation 627x + 1001y = 11. Prove that your list of solutions is complete. (5p)