2002 AMC 10B Problems/Problem 6

Problem

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

$\mathrm{(A) \ } \text{none}\qquad \mathrm{(B) \ } \text{one}\qquad \mathrm{(C) \ } \text{two}\qquad \mathrm{(D) \ } \text{more than two, but finitely many}\qquad \mathrm{(E) \ } \text{infinitely many}$

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 $n$ . $\mathrm{ (B) \ }$

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2002 AMC 10B Problems/Problem 6

Problem

Solution