Definitions Flashcards
Even Integer
An integer n is even if n=2a for some integer a is an element of Z
Odd integer
An integer n is odd if n=2a+1 for some integer a is an element of Z
Parity
Two integers have the same parity if they are both even or they are both odd. Otherwise they have opposite parity.
a | b
Suppose a and b are integers. We say that a divides be, written a | b, if b=ac for some c is an element of Z. In this case we would also say that a is advisor of b and that b is a multiple of a.
Prime natural number
A natural number n is prime if it has exactly two positive divisors, 1 and n.
Composite natural number
A natural number n is is composite if it factors as n=ab where a,b > 1.
Greatest common divisior
Greatest common divisor of integers a and b, denoted gcd (a,b), is the largest integer that divides both a and b.
Least common multiple
The least common multiple of non-zero integers a and b, denote lcm (a,b), is the smallest positive integer that is a multiple of both a and b.
Integers
Suppose a and b are integers. Then a + b is an element of Z, a - b is an element of Z, and ab is an element of Z.
Quotient Theory
Given integers a and b with b>0, there exists unique integers q and r for which a=qb+r and 0 _
(n+1
k) = …
(n + (n
k) + k-1)
n choose k
If n and k are integers, then n denotes the number k of subsets that can be made by choosing k elements from a set with n elements. The symbol n is read “n choose k.”
negate
Negate
Square of opposition
Equivalent statements
Contrapositive
Equivalencies for p implies q
Binomial Theorem
