Math 540 Information for Test 2, Wednesday, Nov. 13, 2013
Covers Homework Assignments #59, and lectures through 11/4/13.
Chinese remainder theorem
Math 540 Information for Final Exam,
Friday, Dec. 20, 2013, 1:30 pm, 454 Snow Hall
Covers all Homework Assignments (#112), and all lectures.
Please refer to all information for Tests 1 and 2. You are responsible for the proofs
listed for those tests. List
Math 540 Information for Test 1
Test 1, Wednesday, Oct. 2, 2013
Covers Chapters 1 and Sections 2.1.1 and 2.3.1 of textbook, Homework
Assignments #14, and lectures through 9/20/13.
You will be asked to:
State theorems. You should be able
MATH 540 Additional Homework Problems
Refer to Homework Assignment page for due dates of individual problems.
1. Prove or disprove: Let a, b, c be nonzero integers. If a|b, then a|bc.
2. Prove or disprove: Let a, b, c be nonzero integers. If a|c and b|c,
Greatest Common Divisors
The greatest common divisor (m, n) of integer m and n is the largest integer which divides both m
The greatest common divisor can be found using the Euclidean algorithm, which is a process of
MATH 540 Notes
Theorem [Fundamental Theorem of Arithmetic] Let n N, n 2. Then there exist prime
numbers p1 p2 ps such that n =
pi . Furthermore, this factorization is unique,
qi where the qi are primes and q1 q2 qt , then t = s and for all
A prime number is an integer n > 1 whose only positive divisors are 1 and n. An integer greater than
1 which is not prime is composite.
Euclid showed that there are innitely many primes.
The Prime Number Theorem says that the nu