PROBLEM SET 1 (DUE IN LECTURE ON SEP 18)
(All Theorem and Exercise numbers are references to the textbook by Apostol; for instance
“Exercise I 3.5-5” means Exercise 5 in section I 3.5.)
Problem 1. Prove Theorem I.5 (using Axioms 1-6 and Theorems I.1-I.4).
Problem 2. Prove Theorem I.6 (using Axioms 1-6 and Theorems I.1-I.5).
Problem 3. Do Exercise I 3.5-5.
Problem 4. Do Exercise I 3.5-7.
Problem 5. Do Exercise I 3.12-1. (This is in a later section, but you should still only need
Axioms 1-9 and Theorems I.1-I.25.)
Problem 6. Do part (b) of Exercise I 4.4-1.
Problem 7. Do Exercise I 4.4-11. (Hint: induct on the statement “Every integer m with
1 < m ≤ n is either a prime or a product of primes.”)
Problem 8. Do Exercise I 4.7-12. (Hint: compute the first few values of this sum to guess
the general formula, then prove it.)
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