2002 AMC 12B Problem 3

Problem 3 of 25EasierAlgebra Number Theory

For how many positive integers

n

n^2-3n+2

a prime number?

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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.

Concepts: factoring · prime

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