Today's definitions: An integer n is even if there exists an integer k such that n = 2k. An integer n is odd if there exists an integer k such that n = 2k + 1. Every integer is either even or odd (and no integer is both). An integer n is threven if there exists an integer k such that n = 3k. An integer n is throver if there exists an integer k such that n = 3k + 1. An integer n is thrunder if there exists an integer k such that n = 3k - 1. Every integer is either threven, throver, or thrunder (and no integer is two or three of those properties).

Due at the beginning of class Friday 7 October:

1. Write careful proof that the sum of two odd integers is even.

2. Compute several examples of the product of a throver number and a thrunder number. Are the products all threven, all throver, all thrunder, or a mix?

3. Fill in the blank and then write careful proof: The product of a throver number and a thrunder numbers is a _______ number.