2006 UNCO Math Contest II Problems/Problem 8
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.
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
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