The sum of a natural number n and its square equals the product of the first three prime numbers. What is n?

Answer 1

n + n^2 = (2)(3)(5)

n + n^2 = 30

n^2 + n - 30 = 0

(n - 5)(n + 6) = 0

n - 5 = 0 or n + 6 = 0

n = 5 or n = -6

Since -6 is not a natural number, the answer is n = 5 Remember: 1 is neither prime nor composite number, and 2 is the only even Prime number. -6 is an integer, but is not a natural number The set of natural numbers is: N = {1, 2, 3, 4,...} The set of whole numbers is: W = {0, 1, 2, 3,...} The set of all integers is: I = {..., -3, -2, -1, 0, 1, 2, 3, ...} The set of all Rational numbers is: Q = {a/b|a,b are integers, and b is different than 0} The decimal names for elements of Q are:

(1) terminating, (2) nonterminating with a repeating block Examples: 1/2 = 0.5 and 1/3 = 0.333...

The set of all Irrational Numbers is: S = {x|x has a decimal name which is nonterminating and doesn't have a repeating block} Examples of irrational numbers include 0.101001000..., pi and square root of 2 Q and S have no common elements. All these numbers are called real numbers.