AoPSWiki

Want to learn how to tackle those tough AMC/AIME/Olympiad counting and probability problems? Check out Art of Problem Solving's Intermediate Counting & Probability by David Patrick.

Personal tools

Search

Toolbox

2002 AMC 12B Problems/Problem 3

From AoPSWiki

Problem

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

$\mathrm{(A)}\ \text{none}\qquad\mathrm{(B)}\ \text{one}\qquad\mathrm{(C)}\ \text{two}\qquad\mathrm{(D)}\ \text{more\ than\ tw...$

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 $1\ \mathrm{(B)}$ .

See also

2002 AMC 12B (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25

Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/2002_AMC_12B_Problems/Problem_3"

Category: Introductory Number Theory Problems

Do you have what it takes to be the next brilliant trader, researcher, or developer at Jane Street Capital? Find out in the Careers in Mathematics Forum.

© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us