Chapter 1.1, Problem 52ES

To determine

(a)

Find a counterexample to prove that the inductive argument in exercise $31$ is incorrect.

To determine

(b)

Find the counterexample of the statement is as follows.

The following equations show that $n^2-n+11$ is a prime number for all counting numbers $n=1,2,3,4,\mathrm{...}$