problem: The function $f (n) = n^2 + n + 17$ for $0 \leq n \leq 15$ generates prime numbers. What is the value of $f (10)-f (9)$?
solution: We have $f(10)-f(9) = (10^2+10+17)-(9^2+9+17) = 10^2-9^2+10-9 = 100-81+1 = \boxed{20}$.