Every nonempty set of positive integers contains a smallest number.
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.
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.