Homework:
Problems marked with an asterisk (*) are for extra credit.

HW 1 (due 02/05 in class) [solutions]

Chapter 1: Ex 1.1, 1.3, 1.4

Chapter 2: Ex 2.1, 2.3 a) and b), 2.4

HW 2 (due 02/12 in class) [solutions]

Chapter 3: Ex 3.1, 3.2, 3.3

Chapter 4: Ex 4.2 a), b), d) only

Chapter 5: Ex 5.1, 5.3, 5.5 a) and b) only

HW 3 (due 02/19 in class) [solutions]

Chapter 6: Ex 6.1, 6.2, 6.3, 6.4 a) only

Chapter 7: Ex 7.2, 7.3, 7.4

HW 4 (due 02/26 in class) [solutions]
 Find the primepower factorization of 20!
 How many zeroes are at the end of 50! in decimal notation? Explain!
 Which positive integer numbers have exactly three positive divisors? Which have exactly four positive divisors?
 Show that if a and b are positive numbers such that a3b^{2}, then ab.

Chapter 7: Ex 7.5

Chapter 8: Ex 8.2, 8.3, 8.4

HW 5 (due 03/04 in class) [solutions]

Chapter 9: Ex. 9.1, 9.4

Chapter 10: Ex 10.1, 10.2, 10.3 (a)

Chapter 11: Ex 11.1, 11.2

HW 6 (due 03/11 in class) [solutions]

Chapter 11: Ex 11.5, 11.8, 11.9, 11.10, 11.11 a)
 What should the check digit be to complete the following ISBN: 019081082 ?
 Determine if the ISBN 1092312213 is valid?

HW 7 (due 03/25 in class) [solutions]

Chapter 19: Ex 19.1, 19.3
 Find the sum of the positive divisors of each of the following integers: 2^{100}, 196, and 20!
 Which positive integers have an odd number of positive divisors?
 Find the smallest positive integer n with τ(n)=3.
 Which positive integers have exactly four positive divisors?
 Show that no two positive integers have the same product of divisors.^{*}
 Find the following values of the Moebius μ function: μ(12), μ(30)
 Show that for any positive integer n we have μ(n) μ(n+1) μ(n+2) μ(n+3)=0.
 Is it possible for the Moebius μ function to vanish for 5 consecutive values of n?
 Use the Moebius inversion formula to express the Euler φ function in terms of the Moebius μ function.
 Chapter 13: Ex 13.3

HW 8 (due 04/15 in class) [solutions]

Chapter 17: Ex 17.1, 17.2, 17.4

Chapter 18: 18.1, 18.2
 Find the primes p and q if pq=4,386,607 and φ(pq)=4,382,136. Explain the method you have used.

HW 9 (due 04/22 in class) [solutions]

Chapter 20: Ex 20.1, 20.2, 20.3, 20.4, 20.6, 20.7 a) only, 20.8

Chapter 21: Ex 21.1, 21.3

HW 10 (due 04/29 in class)

Chapter 22: Ex 22.3

Chapter 23: Ex 23.1, 23.3, 23.5

Chapter 24: Ex 24.1, 24.2, 24.4, 24.6, 24.7, 24.9

Chapter 25: Ex 25.2 (bonus problem)

HW 11 (due 05/6 in class; bonus problems)

Chapter 25: Ex 25.3, 25.5

Chapter 26: Ex 26.1, 26.6