2002 AMC 12B Problem 3

Attempt Problem 3 of the 2002 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 12B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

none

one

two

more than two, but finitely many

infinitely many

Answer: B

Concepts:factoring prime

Difficulty rating: 1120

Solution:

Factor $n^2-3n+2=(n-1)(n-2).$ For $n\ge4$ both factors exceed $1,$ so the value is composite. Checking $n=1,2,3$ gives $0,$ $0,$ and $2.$ Only $n=3$ yields a prime, so there is exactly one such $n.$

Thus, the correct answer is B.

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