Definitions

Parity

An integer x is even if there is an integer k such that x = 2k. An integer x is odd if there is an integer k such that x = 2k+1.

The parity of a number is whether the number is odd or even.

Rationality

A number r is rational if there exist integers x and y such that y ≠ 0 and r = x/y.

Division

An integer x divides an integer y if and only if x ≠ 0 and y = kx, for some integer k. The fact that x divides y is denoted x|y. If x does not divide y, then that fact is denoted x∤y. If x divides y, then y is said to be a multiple of x, and x is a factor or divisor of y.

Prime

An integer n is prime if and only if n > 1, and the only positive integers that divide n are 1 and n.

An integer n is composite if and only if n > 1, and there is an integer m such that 1 < m < n and m divides n.