Solutions to Exercises in the Introduction of How To Prove It by Daniel J Velleman.
Problem (2): Make some conjectures about the values of for which is prime or the values of for which is prime. (You might start by making a table similar to Figure 1) .
Okay, first lets make a table:
Now let us make (up) some conjectures:
(1) For any value of , is not a prime number.
(2) For any value of , is a prime number if is a prime.
Note that conjecture 1 is true because will always be an even number. Conjecture 2 is not true since it breaks down when