Problem:
For how many positive integers is a prime number?
Answer Choices:
A. none
B. one
C. two
D. more than two, but finitely many
E. infinitely many
Solution:
If , then
is the product of two integers greater than 1 , and thus is not prime. For , 2 , and 3 we have, respectively,
Therefore, is prime only when . The answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions