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2002 AMC 10B Problems/Problem 6

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Problem

For how many positive integers n is n^2-3n+2 a prime number?

\mathrm{(A) \ } \text{none}\qquad \mathrm{(B) \ } \text{one}\qquad \mathrm{(C) \ } \text{two}\qquad \mathrm{(D) \ } \text{mor...

Solution

Factoring, n^2-3n+2=(n-1)(n-2). As primes only have two factors, 1 and itself, n-2=1, so n=3. Hence, there is only one positive integer n. \mathrm{ (B) \ }

See Also

2002 AMC 10B (ProblemsResources)
Preceded by
Problem 5
Followed by
Problem 7
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Looking for a challenging geometry text? Preparing for MATHCOUNTS or the AMC exams? Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
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