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- StudyBlue
- Virginia
- Lynchburg College
- Mathematics
- Mathematics 405
- Cline
- Abstract Algebra

Lewis W.

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17
Well Ordering Principle

Every nonempty set of positive integers contains a smallest number.

Division Algorithm

Let a and b be integers with b > 0. Then there exist unique integers a and r with the property that a = bq +r where 0<=r<=b

Greatest Common Divisor/Relatively Prime Integers

The *greatest common divisor* of two nonzero integers a and b is the largest of all common divisors of a and b. We denote this integer by gcd(a,b). When gcd(a,b) = 1, we say a and b are *relatively prime*.

a mod n

Let *n *be a fixed positive integer. For any integer *a*, *a* mod *n* is the remainder upon dividing *a *by *n*.

Modular Equations

If *a *and *b *are integers and *n *is a positive integer, we write *a* = *b* mod n when *n *divides *a - b*.

First Principle of Mathematical Induction

Let S be a set of integers containing a. Suppose S has the property that whenever some integer n >= a belongs to S, then the integer n + 1 also belongs to S. Then, S contains every integer greater than or equal to a.

Second Principle of Mathematical Induction

Equivalence Relation

Partition

Function (Mapping)

Composition of Functions

One-to-One Function

Function from A onto B

Binary Operation

Group

Abelian

Least Common Multiple

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