Number Theory: Problem 6

Solution to (a)

Let's choose $$n = 9$$. Then $$n^2 + 9n - 2 = 9^2 + 9 * 9 -2 = 160$$. Total number of people who get the muffins is 20 and each person will get 8 muffins. So $$n = 9$$ is a solution.