Chapter 4.2, Problem 8MC

A perfect square is a number that can be written as $n^2$, where n is a whole number.

a. Check that the following statement is true for 4 different cases. How many cases do you need to try to conclude that the statement is true?

“1 plus the product of any four consecutive whole numbers is always a perfect square”

b. Prove that the sum of first n odd numbers is a perfect square.

c. Find all perfect square numbers that are 9 more than some prime number. Explain how you know that you found all such square numbers. (Hint: Recall from Chapter 3 that $a^2-b^2=\left(a-b\right)\left(a+b\right).$)