Difference between revisions of "2002 AMC 10B Problems/Problem 6"
(New page: == Problem == 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)...) |
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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> | 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== | ||
| + | {{AMC10 box|year=2002|ab=B|num-b=5|num-a=7}} | ||
| + | |||
| + | [[Category:Introductory Number Theory Problems]] | ||
Revision as of 13:58, 27 December 2008
Problem
For how many positive integers 
is 
a prime number?
Solution
Factoring, 
. As primes only have two factors, 
and itself, 
, so 
. Hence, there is only one positive integer . 
See Also
| 2002 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
