Solutions to Homework Set 3 (Solutions to Homework Problems
If GCD(a n) = 1
3 Congruence
Theorem 3.3 If a ? b mod n then b = a + nq for some integer q Theorem 3.12 If ab ? ac mod n and if gcd(a
Divisibility Memorize: If a and b are integers we say that a divides b
b ? and the remainder r is a(mod b). (discussed below). Prime Numbers. Memorize: An integer p > 1 is called prime if its only positive divisors are 1 and
CHAPTER 2 RING FUNDAMENTALS 2.1 Basic Definitions and
Note that ab need not equal ba; if this holds for all a b ? R
Congruence and Congruence Classes
If a ? b (mod n) and c ? d (mod n) then. (i) a + c ? b + d (mod n). (ii) ac ? bd (mod n) . Proof. (i) By the definition of congruence there are integers s
Prove: For integers a b and positive integer m
https://www.math.fsu.edu/~wooland/mad2104/integers/proofPDFs/glmmrgg.pdf
3 Congruence
Theorem 3.3 If a ? b mod n then b = a + nq for some integer q Theorem 3.12 If ab ? ac mod n and if gcd(a
Math 3450 - Homework # 3 Equivalence Relations and Well-Defined
(d) S is the set of subsets of N where A ? B if and only if A ? B. Is the operation a ? b = ab a well-defined operation on Zn?
3. Equivalence Relations 3.1. Definition of an Equivalence Relations
A relation R on a set A is an equivalence relation if and If a ? b(mod m) then a ? b = k · m for some integer k. Thus
Math 110 Homework 1 Solutions
Jan 15 2015 (b) The greatest common divisor is the largest positive integer d which ... result: If p is prime and p divides a product of integers ab
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