Difference between revisions of "1996 AIME Problems/Problem 3"

(Solution)
(Solution)
Line 3: Line 3:
  
 
== Solution ==
 
== Solution ==
We can factor that into
+
{{solution}}
 
 
<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 15:05, 24 September 2007

Problem

Find the smallest positive integer $n$ for which the expansion of $(xy-3x+7y-21)^n$, after like terms have been collected, has at least 1996 terms.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also