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| − | == Problem ==
| + | #REDIRECT[[2002 AMC 12B Problems/Problem 3]] |
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| − | For how many positive integers <math>n</math> is <math>n^2-3n+2</math> a prime number?
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| − | <math> \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} </math>
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| − | == Solution ==
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| − | Factoring, <math>n^2-3n+2=(n-1)(n-2)</math>. As primes only have two factors, <math>1</math> and itself, <math>n-2=1</math>, so <math>n=3</math>. Hence, there is only one positive integer <math>n</math>. <math>\mathrm{ (B) \ }</math>
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| − | ==See Also==
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| − | {{AMC10 box|year=2002|ab=B|num-b=5|num-a=7}}
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| − | [[Category:Introductory Number Theory Problems]] | |
