Let n be an integer. Use a direct proof to show that if n +4 is a perfect square, then 4n+20 is equal to the sum of two perfect squares. Make sure to include the introduction, body, and conclusion. Clearly state your reasoning for all statements and use a two-column proof for the body whenever possible. You should include an intro, body (in two-column format), and a conclusion. (Hint: Multiply n+ 4 by 4.)

Click and drag the steps in the correct order to show that if n is a positive integer, then n is even if and only if 7n +4 is even. Suppose that n is even. Suppose that n is not even. Thus, 7n + 4 = 14k +10= 2(7k+5). Then, 7n + 4 = 14k + 2 = 2(7k + 1). Since n is even, it can be written as 2k for some integer k. This is 2 times an integer; so it is even as desired. Then, n can be written as 2k +1 for some integer k. Thus, 7n + 4 = 14k +11 = 2(7k+5)+1. Then, 7n + 4 = 14k + 4 = 2(7k+ 2). This is 1 more than 2 times an integer, so it is odd. Reset

The sum of an integer and 4 less than that integer is even.

Write the following statement as a mathematical statement. Use variable names to denote arbitrary numbers in the domain. Your statements and should be expressed using algebra. "There is no largest integer."