2002 AMC 12B Problems/Problem 3

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

$n^2 - 3n + 2 = (n-2)(n-1)$ , which is the product of two integers greater than $1$ if $n \ge 4$ . When $n = 1,2$ , the expression evaluates to $0$ ; when $n = 3$ it evaluates to be $2$ , a prime number. The answer is $1\ \mathrm{(B)}$ .

2002 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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2002 AMC 12B Problems/Problem 3

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