# The Fundamental Theorem of Arithmetic and Prime Factors

Not what you're looking for?

See the attached file.

1. Prove the following lemma.

Lemma

Suppose that m and n are natural numbers > 1 and that p is a prime number.

The following statements are equivalent:

a. p is a prime factor of m or p is a prime factor of n.

b. p is a prime factor of m*n

Also Use Theorem:

The Fundamental Theorem of Arithmetic.

2. Prove the following corollary. You may use the lemma for this.

Corollary.

Suppose that n is a natural number > 1. Then the following statements are

equivalent:

a. p is a prime factor of n.

b. p is a prime factor of n^(1/2).

##### Purchase this Solution

##### Solution Summary

The fundamental theorem of arithmetic and prime factors are investigated and the details are discussed. The solution is detailed and well presented.

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Probability Quiz

Some questions on probability

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts