5. (10 points) Consider a world in which the only numbers are even numbers, called the [E-zone. In the E-zone, integers can only be factored if they are the product of even numbers. Therefore, we call a number an E-prime if it is positive and it cannot be factored into two or more even numbers. (a) Find the smallest three E-primes. (b) Prove that every number in the [E-zone can be factored into a product of E-primes. (c) Find three different factorization of 180 into E-primes. (d) Some even numbers have only one factorization into E-primes. For example, 12 can only be factored into 2 - 6 (or 6 - 2, which we consider to be the same factorization). Give a complete characterization of all even numbers that have VAT 1395 Assignment 2 3 only one factorization into E-primes. Briefly explain your answer (it does not need to be a formal proof)