Difference between revisions of "1996 AIME Problems/Problem 3"
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== Solution == | == Solution == | ||
| + | We can factor that into | ||
| + | |||
| + | <math>(y-3)^n(x+7)^n</math> | ||
| + | |||
| + | Now that has at least 1996 terms. Therefore, each of the two factors has at least <math>\dfrac{1996}{2}=998</math> terms. When y-3 has x terms, n=x-1. Therefore, n=998-1=997 | ||
== See also == | == See also == | ||
* [[1996 AIME Problems]] | * [[1996 AIME Problems]] | ||
Revision as of 15:04, 24 September 2007
Problem
Find the smallest positive integer 
for which the expansion of 
, after like terms have been collected, has at least 1996 terms.
Solution
We can factor that into
Now that has at least 1996 terms. Therefore, each of the two factors has at least 
terms. When y-3 has x terms, n=x-1. Therefore, n=998-1=997
