2006 UNCO Math Contest II Problems/Problem 8
Problem
Find all positive integers such that is a prime number. For each of your values of compute this cubic polynomial showing that it is, in fact, a prime.
Solution
Factoring, we get . Thus, we must have that either or equal to . If we have equal to 1, we have . Plugging back in the polynomial, we get , which is a prime, so works. If is equal to one, we have , so or . Plugging both back in the polynomial, we get and , respectively. is a prime, but is not, so works. Thus, the answer is
See Also
2006 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
All UNCO Math Contest Problems and Solutions |