Difference between revisions of "2002 AMC 10B Problems/Problem 6"

Latest revision as of 16:36, 28 July 2011

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-== Problem ==
+#REDIRECT[[2002 AMC 12B Problems/Problem 3]]
-For how many positive integers <math>n</math> is <math>n^2-3n+2</math> a prime number?
-<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>
-== Solution ==
-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>